a multi-wavelength study of fast winds from central stars ...2 the possible non-smooth nature of the...
TRANSCRIPT
UNIVERSITY COLLEGE LONDON
Faculty of Mathematics & Physical Sciences
Department of Physics & Astronomy
A Multi-Wavelength Study
Of Fast Winds From
Central Stars Of Planetary Nebulae
Thesis submitted for the
Degree of Doctor of Philosophy
University College London
by
Simon Elsdon Hodges
Supervisors: Examiners:
Prof. Raman Prinja Prof. Allan Willis
Prof. Ian Howarth Dr. Ian Stevens
June 15, 2011
This thesis is dedicated to...
Mum & Dad
Abstract
Structure has been observed in the stellar outflows of hot, luminous OB stars through
the temporal spectral analysis of UV data: the absorption troughs of wind-accelerated P-
Cygni profiles of certain UV ‘super-ions’, particularly the P v λλ 1118, 1128 doublet, have
revealed the presence of additional absorption components which have been observed to
migrate through the wind. Similar P-Cygni profiles have also been observed in the the UV
spectra of Central Stars of Planetary Nebulae (CSPNs), but detailed temporal analysis of
CSPN outflows has been frustrated due to a lack of substantial time-series data. However,
the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite has provided high-resolution
time-series data for CSPNs, and therefore the nature of the time-variance of UV P-Cygni
profiles can be investigated. To this end FUSE spectroscopic data has been obtained,
and certain key UV resonance lines, as found in the stellar wind, have been subjected
to various time-series analysis tools including Time Variance Spectra (TVS) and Fourier-
based periodicity analysis.
Also, optical time-series data of young CSPNs has been obtained via the ESO High-
Accuracy Radial velocity Planetary Searcher (HARPS) spectrograph, and therefore similar
temporal analysis has been carried out into the possible appearance of time-varying struc-
ture of Helium lines found in the deep photospheric regions of the atmosphere with the
aim of detecting the presence of modulated structure at the base of the stellar wind – with
the aim of discovering a causal mechanism for the higher wind-related phenomena.
The presence of such structure in the stellar outflows of CSPNs (and likewise, OB
stars) suggests that non-LTE stellar atmosphere analysis techniques – such as the Sobolev
with Exact Integration (SEI) method used within this thesis – which assume a spherically
smooth wind may provide inaccurate levels of mass loss from the stellar atmosphere; also,
2
the possible non-smooth nature of the wind is considered from the viewpoint of possess-
ing a more porous ‘clumped’ material which would also have an affect upon mass loss
determinations, a key factor in the understanding of the latter stages of stellar evolution.
Acknowledgements
I would like to take this opportunity to thank my PhD supervisor, Professor Raman
Prinja, for guidance – and above all, patience – as I’ve endeavoured to complete this thesis.
I am indebted to a small and select group of people whose help and advice through the
many computer-related trials and tribulations has been invaluable: Dr Adam Burnley, for
acting as my chaperone in La Silla on my first observing trip; Dr Dugan Witherick, who
first set me up in my temporal analyses; Dr Fabrizio Sidoli, for help far beyond the call
of duty in dealing with innumerable computing crises; Dr Matt North, for his patience in
getting this technophobe to stick with given tasks by taking things one step at a time; Dr
Samantha Searle, for her encouragement; and finally Dr-in-waiting Joanna Fabbri, for all
her help in getting this work onto the pages of latex in some kind of order, and above all,
for simply being around and listening to my woes, even when she has had her own terrific
tome to complete...
4
I, Simon Elsdon Hodges, confirm that the work presented in this thesis is my own.
Where information has been derived from other sources, I confirm that this has been
indicated in the thesis.
“O, there’s so much I don’t know about astrophysics – I wish I’d read that book by
that wheelchair guy.”
Homer J. Simpson – Explorer in the Third Dimension
Contents
Table of Contents 6
List of Figures 10
List of Tables 22
1 Introduction 24
1.1 Introduction to Planetary Nebulae . . . . . . . . . . . . . . . . . . . . . . . 24
1.1.1 Hydrogen-rich CSPNs . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2 The Introduction of Stellar Winds . . . . . . . . . . . . . . . . . . . . . . . 29
1.2.1 The Observation of Stellar Winds . . . . . . . . . . . . . . . . . . . . 29
1.3 The Formation of Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.1 Line scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.2 Line emission by recombination . . . . . . . . . . . . . . . . . . . . . 31
1.3.3 Line emission for collisional- or photo-excitation . . . . . . . . . . . 31
1.3.4 Pure absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.5 Masering by stimulated emission . . . . . . . . . . . . . . . . . . . . 32
1.4 P Cygni Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.4.1 The Formation of P Cygni Profiles . . . . . . . . . . . . . . . . . . . 33
1.5 Mass-Loss Studies from P Cygni Profiles . . . . . . . . . . . . . . . . . . . . 34
1.6 Spectroscopic Investigations into Central Stars of Planetary Nebulae . . . . 35
1.6.1 Further Considerations of Wind-born Metal Lines & the Contribu-
tion of ‘Clumping’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.6.2 FUSE & the Contribution of UV Resonance Line Modelling . . . . . 43
1.6.3 Introducing the Concepts of ‘Clumping’ . . . . . . . . . . . . . . . . 46
6
Contents 7
1.6.4 The Additional Effects of Porosity . . . . . . . . . . . . . . . . . . . 47
1.7 Investigations into Variability in Stellar Winds from OB Stars . . . . . . . . 50
1.8 From O Stars...to Central Stars: Research Objectives . . . . . . . . . . . . . 52
2 Mathematical techniques 53
2.1 Equivalent Width (EW) Measurements . . . . . . . . . . . . . . . . . . . . . 53
2.2 Spectral Time Variance Analysis . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.1 Temporal Variance Spectra (TVS) . . . . . . . . . . . . . . . . . . . 54
2.2.2 Greyscale I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.2.3 Two-dimensional Fourier analysis: power spectra . . . . . . . . . . . 57
2.2.4 Greyscale II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3 Analysing Line Profiles within the Wind: SEI Code . . . . . . . . . . . . . . 61
2.3.1 The SEI Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.4 A Brief Introduction & Description of TLUSTY . . . . . . . . . . . . . . . . 68
2.4.1 Accelerated Lambda Iteration (ALI) . . . . . . . . . . . . . . . . . . 69
2.4.2 Simplification through Super-levels . . . . . . . . . . . . . . . . . . . 72
2.4.3 The Incorporation of the TLUSTY Models into the SEI Code . . . . 73
2.4.4 Example of an SEI Model Fit – Description of Panels . . . . . . . . 74
3 NGC 6543 77
3.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.1.1 The Target – NGC 6543 . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2 FUSE & Time-Series Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2.1 The Instrument Design . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.2.2 Observing Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.2.3 The In-house FUSE Data Reduction Pipeline . . . . . . . . . . . . . 87
3.2.4 The FUSE Time-series Data of NGC 6543 . . . . . . . . . . . . . . . 88
3.3 Evidence of Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.1 Discrete Absorption Components . . . . . . . . . . . . . . . . . . . . 96
3.4 Modulated or Cyclical Behaviour . . . . . . . . . . . . . . . . . . . . . . . . 100
3.5 Line Synthesis & Optical Depths . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5.1 Errors Inherent in SEI Mqi(w) Calculations . . . . . . . . . . . . . . 107
3.5.2 The Case for Clumping via CMFGEN . . . . . . . . . . . . . . . . . 109
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Contents 8
4 FUSE Survey 118
4.1 Fragmented Time-series Objects . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1.1 NGC 6826 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1.2 IC 2149 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1.3 IC 418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.1.4 IC 4593 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2 Time-Averaged Spectra & SEI Modelling . . . . . . . . . . . . . . . . . . . 123
4.2.1 Data Source & Ion Species – NGC 6826 . . . . . . . . . . . . . . . . 124
4.2.2 SEI Model Fits – NGC 6826 . . . . . . . . . . . . . . . . . . . . . . 124
4.2.3 Data Source & Ion Species – IC 2149 . . . . . . . . . . . . . . . . . . 128
4.2.4 SEI Model Fits – IC 2149 . . . . . . . . . . . . . . . . . . . . . . . . 128
4.2.5 Data source & Ion Species – IC 418 . . . . . . . . . . . . . . . . . . 131
4.2.6 SEI Model Fits – IC 418 . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.2.7 Data Source & Ion Species – IC 4593 . . . . . . . . . . . . . . . . . . 134
4.2.8 SEI Model Fits – IC 4593 . . . . . . . . . . . . . . . . . . . . . . . . 135
4.3 Time Variability Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.3.1 Time Variability – NGC 6826 . . . . . . . . . . . . . . . . . . . . . . 138
4.3.2 Time Variability – IC 2149 . . . . . . . . . . . . . . . . . . . . . . . 142
4.3.3 Time Variability – IC 418 . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3.4 Time Variability – IC 4593 . . . . . . . . . . . . . . . . . . . . . . . 154
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5 ESO Optical Data 160
5.1 Introduction – ESO Time-series Objects & their observation . . . . . . . . . 160
5.1.1 Hen 2-138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.1.2 Hen 2-131 & NGC 2392 . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.2 European Southern Observatory 3.6 m Telescope & the HARPS Spectrograph167
5.2.1 Data Reduction Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.2.2 ESO Time-series Optical Data . . . . . . . . . . . . . . . . . . . . . 168
5.3 Time-Averaged Fast-Wind Characteristics . . . . . . . . . . . . . . . . . . . 170
5.3.1 Variety of Absorption Lines . . . . . . . . . . . . . . . . . . . . . . . 170
5.3.2 Ion species: Hen 2-138 . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.3.3 SEI Model Fits – Hen 2-138 . . . . . . . . . . . . . . . . . . . . . . . 171
Contents 9
5.3.4 CMFGEN Analysis of Hen 2-138 . . . . . . . . . . . . . . . . . . . . 173
5.3.5 Ion Species - Hen 2-131 . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.3.6 SEI Model Fits - Hen 2-131 . . . . . . . . . . . . . . . . . . . . . . . 182
5.3.7 Ion Species - NGC 2392 . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.3.8 SEI Model Fits - NGC 2392 . . . . . . . . . . . . . . . . . . . . . . . 186
5.4 Time Variable Characteristics of the CSPN Winds . . . . . . . . . . . . . . 189
5.4.1 Equivalent Width Measurements – Hen 2-138 . . . . . . . . . . . . . 189
5.4.2 Equivalent Width Measurements – Hen 2-131 . . . . . . . . . . . . . 190
5.4.3 Equivalent Width Measurements – NGC 2392 . . . . . . . . . . . . . 191
5.4.4 Time Variance Spectra (TVS) – Hen 2-138 . . . . . . . . . . . . . . 191
5.4.5 Time Variance Spectra (TVS) – Hen 2-131 . . . . . . . . . . . . . . 192
5.4.6 Time Variance Spectra (TVS) – NGC 2392 . . . . . . . . . . . . . . 193
5.4.7 Fourier Analysis & Signal Selection . . . . . . . . . . . . . . . . . . . 194
5.4.8 Fourier Analysis – Hen 2-138 . . . . . . . . . . . . . . . . . . . . . . 195
5.4.9 Fourier Analysis – Hen 2-131 . . . . . . . . . . . . . . . . . . . . . . 196
5.4.10 Fourier Analysis – NGC 2392 . . . . . . . . . . . . . . . . . . . . . . 207
5.4.11 Greyscale Representations of Phased Periods – Hen 2-138 . . . . . . 208
5.4.12 Greyscale Representations of Phased Periods – Hen 2-131 . . . . . . 210
5.4.13 Greyscale Representations of Phased Periods – NGC 2392 . . . . . . 211
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6 Conclusion 222
6.1 Structure in Stellar Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
.1 Appendix A: SEI Plots of Two DAC Sequences . . . . . . . . . . . . . . . . 227
.2 Appendix B: Full 2-D Fourier Spectra Displays . . . . . . . . . . . . . . . . 232
Bibliography 236
List of Figures
1.1 Diagram of stellar evolution of a solar mass star from the main sequence to
a white dwarf, courtesy of R.K. Prinja (via private communication). . . . . 28
1.2 Diagram of components of a UV P Cygni resonance line profile: Lamers &
Cassinelli (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3 The log of the quantity M v∞R⋆0.5 as a function of the log of stellar lumi-
nosity for a selection of hot stars: open triangles, squares, and diamonds
indicate O, B and A supergiants; asterisks indicate lower luminosity class
O stars (giants to main sequence stars). Plus signs are for CSPNs. The
straight line is the indicator of the relation following the 3/2 power of stellar
luminosity: Kudritzki et al. (1997). . . . . . . . . . . . . . . . . . . . . . . . 37
1.4 The wind-momentum-luminosity relation for massive O stars and CSPNs.
Data is derived from Hα analysis (Puls et al. 1996) – P96; similar for CSPNs
(Kudritzki et al. 1997) – K97. Additionally plotted are the wind momenta
for O stars and CSPNs based upon the hydrodynamic models following
post-AGB evolutionary tracks: Pauldrach et al. (2003). . . . . . . . . . . . . 41
2.1 Diagram comparing the strength of a typical spectra absorption line, a,
with its ‘equivalent width’, b. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 Time Variance Spectra (TVS) of the most developed P Cygni absorp-
tion doublets from the F034 time-series spectra of PN NGC 6543: the
well-developed but unsaturated P v λλ 1117.98, 1128.01 doublet is clearly
strongly variable across both the blue and red absorption troughs of the
doublet, showing broad peaks above the dotted 95% confidence line . . . . . 56
10
List of Figures 11
2.3 Full-panel displays of Fourier-based frequency analysis of the blue trough
of the P v doublet, as seen in the F034 spectra of PN NGC 6543, analysed
between −600 – −1100 km s−1, with the ‘dirty’ analysis on the left, and the
‘clean’ analysis (gain = 0.500) on the right. . . . . . . . . . . . . . . . . . . 60
2.4 Greyscale representation of the F034 P v doublet of PN NGC 6543, folded
over a period of 0.172 days – here displayed over three cycles. . . . . . . . . 61
2.5 SEI model fit of the mean spectrum from the F034 dataset of the UV spectra
of the P v doublet, from the Central Star of PN NGC 6543; see text for
detailed descriptions of the individual panels. . . . . . . . . . . . . . . . . . 75
3.1 Hubble Space Telescope image of the ‘Cat’s Eye Nebula’: PN NGC 6543
– taken by the HST Wide Field Planetary Camera 2. The Image is a
composite of three pictures taken at different wavelengths: red - hydrogen-
alpha at 6563 A; blue - neutral oxygen at 6300 A; green - ionised nitrogen
at 6584 A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2 Diagram depicting the Rowland Circle arrangement of gratings and detec-
tors of the FUSE instrument. . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3 ‘Exploded-view’ diagram of the FUSE instrument showing the spatial rela-
tionships between its mirrors, gratings and detectors. . . . . . . . . . . . . . 90
3.4 Diagram of the four FUSE detectors indicating their wavelength-dependent
arrangement of lithium fluoride and silicon carbide coatings. . . . . . . . . . 91
3.5 Mean FUSE spectrum of the central star in NGC 6543 taken from the F034
run in January 2007. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.6 The maximum fluctuation in the Pv λ 1117.98 resonance line compared
with the more stable low velocity regions of O vi λ 1037.62. . . . . . . . . . 92
3.7 Time Variance Spectra (TVS) of the two most developed P Cygni absorp-
tion doublets from the F034 time-series spectra: the well-developed but un-
saturated P v λλ 1117.98,1128.01 doublet (left) is clearly strongly variable
across both the blue and red absorption troughs of the doublet, showing
broad peaks above the dotted 95% confidence line; in contrast, the highly
saturated O vi λλ 1032.97,1038.93 doublet (right) shows a negligible TVS
response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
List of Figures 12
3.8 Greyscale images of the four nights’ optical spectra (2alif section) from the
F034 observation. These are displayed left to right and bottom to top as the
the individual greyscale images chronologically proceed from the bottom of
the image upwards: 13th, 14th January shown bottom left, right; 15th, 16th
January shown top left, right. . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.9 A single greyscale image of the 2alif section spectra of the entire F034 data.
Using this singular format, it is easier to observe the cyclic behaviour of the
DACs present in the P v doublet. . . . . . . . . . . . . . . . . . . . . . . . . 95
3.10 A pair of multi-stacked mean-rectified spectra showing the velocity-space
fluctuations from the mean 2alif spectra of the two DAC sequences – this
method allows for easier identification of the progression of the DACs through
the sequences. The central velocity of each individual blueward DAC is
marked with a red tick – this is the position of the individual velocity mea-
surements taken in order to estimate the acceleration of the DAC through
the wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.11 Plotted progressive velocity tracks of two DAC sequences, each over-plotted
with a least-squares fit of the resultant acceleration. . . . . . . . . . . . . . 99
3.12 Full-panel displays of Fourier-based frequency analysis of the blue trough
of the P v doublet, as seen in the F034 spectra, analysed between −600 –
−1100 km s−1, with the ‘dirty’ analysis on the left, and the ‘clean’ analysis
(gain = 0.500) on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.13 Extracted power spectrum output of a Fourier-based frequency analysis of
the F034 spectra, analysed between −600 to −1000 km s−1(the velocity
range across which the DACs appear to traverse): the top panel shows the
power spectra derived from the ‘dirty’ analysis in black, with the ‘cleaned’
analysis (gain = 0.500) superimposed in red; the bottom panel shows the
cleaned analysis on its own in red, with the highest peak indicating a
strongest signal occurring at ∼ 5.8125 cycles per day. . . . . . . . . . . . . . 102
3.14 Greyscale representation of the F034 P v doublet folded over a period of
0.172 days – here displayed over three cycles. . . . . . . . . . . . . . . . . . 103
3.15 TVS analysis of IUE data of the C iv λλ 1548, 1550 doublet – note the
double/triple nature of the variability response. . . . . . . . . . . . . . . . . 104
List of Figures 13
3.16 SEI fits to the mean P v resonance profiles of the 4 consecutive nights of
the F034 run: 13th, 14th January 2007, top left, right; 15th, 16th January
2007, bottom left, right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.17 SEI model fit of the mean spectrum from the F034 observation. . . . . . . . 106
3.18 A pair of multi-stacked spectra showing the velocity-space progression of
P v doublet DACs for two sequences. . . . . . . . . . . . . . . . . . . . . . 115
3.19 Plot showing the changes of the radial optical depth ratios, τDAC/τmin, for
the two DAC sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.20 CMFGEN model fits of key diagnostic lines for NGC 6543 are shown (from
FUSE and high-resolution IUE spectra), where the superimposed models
have filling-factors of f∞ = 0.06 (solid line), 0.08 (dashed line), and 0.10
(dotted line). Courtesy of Miguel Urbaneja (via private communication). . . 116
3.21 Log plots of the P iv , P v and P vi ion fractions as functions of the blue-
ward wind velocity, for the filling-factor cases of f∞ = 0.06 (solid line), 0.08
(dashed line), and 0.10 (dotted line). Courtesy of Miguel Urbaneja (via
private communication). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1 HST WFPC2 image of PN NGC 6826 (the ‘Blinking Nebula’), showing the
nebula’s gaseous composition with nitrogen (red), hydrogen (green), and
oxygen (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2 Composite MMT near-infrared image of PN IC 2149, made up of exposures
taken via red (2.09 µm), green (2.19 µm), and blue (2.17 µm) filters. . . . . 119
4.3 HST WFPC2 image of PN IC 418 (the ‘Spirograph Nebula’), showing the
nebula’s gaseous composition with nitrogen (red), hydrogen (green), and
oxygen (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.4 HST WFPC2 image of PN IC 4593, with filters depicting different nebula
gases, namely nitrogen ([N ii] - red), helium (Hα - green), and oxygen ([O iii]
- blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.5 Mean FUSE spectra for NGC 6826 highlighted with key resonance lines . . 125
4.6 NGC 6826: SEI model fits for the mean spectra for the P v (l) and O vi (r)
resonance lines shown above, with model fits for S vi (l) and C iii (r) shown
below. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.7 Mean FUSE spectra for IC 2149 highlighted with key resonance lines . . . . 129
List of Figures 14
4.8 IC 2149: SEI model fits for the mean spectra for the P v (l) and O vi (r)
resonance lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.9 Mean FUSE spectra for IC 418 highlighted with key resonance lines . . . . 131
4.10 IC 418: SEI model fits for the mean spectra for the P v (l) and O vi (r)
resonance lines shown above, with model fits for S vi (l) and C iii (r) shown
below. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.11 Mean FUSE spectra for IC 4593 highlighted with key resonance lines . . . . 134
4.12 IC 4593: SEI model fits for the mean spectra for the P v (l) and O vi (r)
resonance lines shown above, with model fits for S vi (l) and C iii (r) shown
below. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.13 NGC 6826: Overplot of P v doublet spectra illustrating the variable nature
of the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 on the
right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.14 NGC 6826: Dual spectra plot depicting Pv doublet with minimum (black)
and maximum (red) absorption. . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.15 TVS analysis plots (below) of the P Cygni profiles of the Pv λλ 1117.98,
1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of NGC 6826,
where the upper panel of each TVS profile depicts the variance statistic,
with changes above the 95% significance level (dotted line) highlighted. The
corresponding greyscale depiction of each line profile’s time-series spectra
is also shown (above) depicting the temporal changes in the (vertically
stacked) individual spectra, all normalised by the corresponding mean pro-
file as shown in the lower panel beneath the TVS significance profile; the dy-
namical range of the greyscales on this page – and all subsequent greyscales
in this chapter – is 0.95 (black) to 1.05 (white). . . . . . . . . . . . . . . . . 140
4.16 Low-resolution greyscale of P v doublet from which approximate mesure-
ments can be taken of both velocity and time index of the blueward pro-
gression of the DAC-like features observed in the greyscale display of the
P1930401 data of PN NGC 6826 in order to estimate the albeit (linear and
therefore approximate) acceleration of the ‘DACs’. . . . . . . . . . . . . . . 142
List of Figures 15
4.17 The two sets of velocity-time coordinates of the DAC-like feature observed
in the low-resoultion greyscale of the NGC 6826 P1930401 UV data are
plotted and a least-squares algorithm has calculated the gradient of the
best-fit line through the points: the acceleration of the first DAC-like feature
is approximated at ∼ 2.4 × 10−2 km s−2; the acceleration of the second is
similarly fitted and approximated at ∼ 2.5 × 10−2 km s−2. . . . . . . . . . . 144
4.18 IC 2149: Overplot of P v doublet spectra illustrating the variable nature
of the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 on the
right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.19 IC 2149: Dual spectra plot depicting P v doublet with minimum (black)
and maximum (red) absorption. . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.20 TVS analysis plots (below) of the P Cygni profiles of the Pv λλ 1117.98,
1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC 2149; the
corresponding greyscale depiction of each lines time-series spectra is also
shown (above). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.21 IC 2149: TVS & greyscale outputs for the P v doublet of the 1st (l) and
3rd (r) nights’ data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.22 A low-resolution greyscale of P v doublet from which an approximate mea-
surement can be taken of both velocity and time index of the blueward
progression of the DAC-like feature observed in the greyscale display of the
P1041401 data of PN IC 2149 in order to estimate the albeit (linear and
therefore approximate) acceleration of the ‘DAC’. . . . . . . . . . . . . . . . 148
4.23 The velocity-time index coordinates as measured from the low-resolution
greyscale of the IC 2149 P1041401 UV data are plotted and a least-squares
algorithm has calculated the gradient of a best line fit through the points:
the linear (and therefore approximate) acceleration of the DAC-like feature
is therefore estimated at ∼ 2.1 × 10−2 km s−2. . . . . . . . . . . . . . . . . . 149
4.24 IC 418: Overplot of P v doublet spectra illustrating the variable nature of
the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 on the
right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.25 IC 418: Dual spectra plot depicting P v doublet with minimum (black) and
maximum (red) absorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
List of Figures 16
4.26 TVS analysis plots (below) of the P Cygni profiles of the Pv λλ 1117.98,
1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC 418; the
corresponding greyscale depiction of each lines time-series spectra is also
shown (above). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.27 IC 418: TVS & greyscale outputs, centred on the stronger red component
of the S iv λλ 1062.66, 1072.97 doublet. . . . . . . . . . . . . . . . . . . . . . 153
4.28 IC 4593: Overplot of P v doublet spectra illustrating the variable nature
of the resonance profile: P v λ 1117.98 . . . . . . . . . . . . . . . . . . . . . 154
4.29 IC 4593: Dual spectra plot depicting P v doublet with minimum (black)
and maximum (red) absorption. . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.30 TVS analysis plots (below) of the P Cygni profiles of the Pv λλ 1117.98,
1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC 4593; the
corresponding greyscale depiction of each lines time-series spectra is also
shown (above). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.31 IC 4593: TVS & greyscale outputs for the S iv λλ 1062.66, 1072.97 doublet. 156
5.1 HST WFPC2 image of PN Hen 2-138, captured via the Hα filter. . . . . . . 161
5.2 HST WFPC2 image of PN Hen 2-131, captured via the Hα filter. . . . . . . 162
5.3 HST WFPC2 image of PN NGC 2392: the different colours of the image
highlight different gases comprising the nebula: nitrogen (red), hydrogen
(green), oxygen (blue), and helium (violet). . . . . . . . . . . . . . . . . . . 163
5.4 Diagram of the ESO HARPS spectrograph system. . . . . . . . . . . . . . . 176
5.5 Mean ESO optical spectral lines of photospheric, fast wind and nebula
regions of Hen 2-138. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.6 Mean far UV spectral lines depicting fast wind features from FUSE & IUE
data of Hen 2-138. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.7 Hen 2-138 UV spectrum (IUE) showing blueward shifted Si iii triplets –
with Si iii singlet at 1312 A also shown – the vertical dashed lines indicate
the spectral rest positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
List of Figures 17
5.8 SEI fits to the Hen 2-138 UV P Cygni profiles of (left to right, top to bot-
tom: Si iv λ 1394, C iv λ 1548, S iv λ 1073, and Al iii λ 1855. The larger
panels display the SEI model fit overlaid upon the observed spectra, and the
smaller panels depict the input photospheric spectra (right) and the derived
radial optical depth profile shown as a function of normalised velocity (left).
The two higher ionisation species (above) require a higher terminal velocity
of 700 km s−1, whereas the two lower ionisation species (below) only require
a terminal velocity of 300 km s−1. . . . . . . . . . . . . . . . . . . . . . . . . 179
5.9 CMFGEN model fits for Hen 2-138 . . . . . . . . . . . . . . . . . . . . . . . 180
5.10 Mean ESO optical resonance lines of photospheric, fast wind, and nebula
regions of Hen 2-131. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.11 Mean far UV spectral lines depicting fast wind features from FUSE & IUE
data of Hen 2-131. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.12 Hen 2-131 UV spectrum (IUE) showing blueward shifted Si iii triplets -
with Si iii singlet at 1312 A also shown - the vertical dashed lines indicate
the spectral rest positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.13 SEI model fits to the Hen 2-131 P Cygni resonance profiles of P v λ 1118,
S iv λ 1073, Si iv λ 1394, and Al iii λ 1855. . . . . . . . . . . . . . . . . . . . 183
5.14 Mean ESO optical resonance lines of photospheric, fast wind, and nebula
regions of NGC 2392. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.15 Mean far UV spectral lines depicting fast wind features from FUSE & IUE
data of NGC 2392. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.16 NGC 2392 UV spectrum (IUE) showing blueward shifted Si iii triplets -
with Si iii singlet at 1312 A also shown - the vertical dashed lines indicate
the spectral rest positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.17 SEI model fits to the NGC 2392 P Cygni resonance profiles of O vi λ 1032,
Nv λ 1239, C iv λ 1548, and P v λ 1118. . . . . . . . . . . . . . . . . . . . . . 187
5.18 Three 18 exposure over-plots of the He i λ 5876 line for (l-r) Hen 2-138,
Hen 2-131, NGC 2392, the individual exposures, taken over ∼ 2.2 days, are
plotted in red, and the mean profile is overlaid in black, so as to further
emphasise the variable nature of the P Cygni profile. . . . . . . . . . . . . . 189
List of Figures 18
5.19 TVS analysis plots (below) of the absorption profile of the He i λ 4026 (l)
and He i λ 4471 (r) optical lines of Hen 2-138, where the upper panel of
each TVS profile depicts the variance statistic, with changes above the 95%
significance level (dotted line) highlighted. The corresponding greyscale
depiction of each line profile’s time-series spectra is also shown (above) de-
picting the temporal changes in the (vertically stacked) individual spectra,
all normalised by the corresponding mean profile as shown in the lower panel
beneath the TVS significance profile; the dynamical range of the greyscales
on this page – and all subsequent greyscales in this chapter – is 0.95 (black)
to 1.05 (white). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.20 TVS analysis plots (below) of the absorption profile of the He i λ 5876 (l)
and C iv λ 5801 (r) optical lines of Hen 2-138; the corresponding greyscale
depiction of each lines time-series spectra is also shown (above). . . . . . . . 199
5.21 TVS analysis plots (below) of the absorption profile of the He i λ 4026 (l)
and He i λ 4471 (r) optical lines of Hen 2-131; the corresponding greyscale
depiction of each lines time-series spectra is also shown (above). . . . . . . . 200
5.22 TVS analysis plots (below) of the absorption profile of the He i λ 5876 (l)
and C iv λ 5801 (r) optical lines of Hen 2-131; the corresponding greyscale
depiction of each lines time-series spectra is also shown (above). . . . . . . . 201
5.23 TVS analysis plots (below) of the absorption profile of the He i λ 4026 (l)
and He i λ 4471 (r) optical lines of NGC 2392; the corresponding greyscale
depiction of each lines time-series spectra is also shown (above). . . . . . . . 202
5.24 TVS analysis plots (below) of the absorption profile of the He i λ 5876 (l)
and C iv λ 5801 (r) optical lines of NGC 2392; the corresponding greyscale
depiction of each lines time-series spectra is also shown (above). . . . . . . . 203
5.25 A display of Fourier power spectra for the optical resonance lines of Hen
2-138: the black shows the uncleaned power spectra and the red shows the
cleaned power spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
List of Figures 19
5.26 Fourier power spectra (left) of the C iv λ 5801 deep photospheric line, and
the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of Hen 2-138:
the uncleaned power spectra is shown in black, with the corresponding
cleaned spectra superimposed in red; Cleaned power spectra of the afore-
mentioned optical lines are also shown separately (right). The dotted lines
indicate the window function frequencies which may provide false power
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
5.27 A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,
He i λ 4471, He i λ 5876 optical lines of Hen 2-138 over -plotted upon each
other – the aim is to strengthen any potential periodicity in the variability
by identifying a peak frequency in more than one line. . . . . . . . . . . . . 205
5.28 A display of Fourier power spectra for the optical resonance lines of Hen 2-
131: the black shows the dirty power spectra and the red shows the cleaned
power spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
5.29 Fourier power spectra (left) of the C iv λ 5801 deep photospheric line, and
the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of Hen 2-131:
the uncleaned power spectra is shown in black, with the corresponding
cleaned spectra superimposed in red; Cleaned power spectra of the afore-
mentioned optical lines are also shown separately (right). The dotted lines
indicate the window function frequencies which may provide false power
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
5.30 A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,
He i λ 4471, He i λ 5876 optical lines of Hen 2-131 over -plotted upon each
other – the aim is to strengthen any potential periodicity in the variability
by identifying a peak frequency in more than one line. . . . . . . . . . . . . 208
5.31 A display of Fourier power spectra for the optical resonance lines of NGC
2392: the black shows the uncleaned power spectra and the red shows the
cleaned power spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
List of Figures 20
5.32 Fourier power spectra (left) of the C iv λ 5801 deep photospheric line, and
the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of NGC 2392:
the uncleaned power spectra is shown in black, with the corresponding
cleaned spectra superimposed in red; Cleaned power spectra of the afore-
mentioned optical lines are also shown separately (right). The dotted lines
indicate the window function frequencies which may provide false power
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
5.33 A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,
He i λ 4471, He i λ 5876 optical lines of NGC 2392 over -plotted upon each
other – the aim is to strengthen any potential periodicity in the variability
by identifying a peak frequency in more than one line. . . . . . . . . . . . . 211
5.34 Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r)
deep-wind lines of Hen 2-138, in which the data has been ‘folded’ over a
period of 0.34 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
5.35 Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r)
deep-wind lines of Hen 2-131, in which the data has been ‘folded’ over a
period of 0.43 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
5.36 Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r)
deep-wind lines of NGC 2392, in which the data has been ‘folded’ over a
period of 0.23 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
5.37 Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r)
deep-wind lines of NGC 2392, in which the data has been ‘folded’ over a
period of 0.30 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
.1 The first four SEI models of the 1st P v DAC-progressive sequence for Hen
2-138: above No. 1 (l), No. 2 (r); below No. 3 (l), No. 4 (r). . . . . . . . . . 227
.2 The second four SEI models of the 1st P v DAC-progressive sequence for
Hen 2-138: above No. 5 (l), No. 6 (r); below No. 7 (l), No. 8 (r). . . . . . . 228
.3 The first four SEI models of the 2nd P v DAC-progressive sequence for Hen
2-138: above No. 1 (l), No. 2 (r); below No. 3 (l), No. 4 (r). . . . . . . . . . 229
.4 The second four SEI models of the 2nd P v DAC-progressive sequence for
Hen 2-138: above No. 5 (l), No. 6 (r); below No. 7 (l), No. 8 (r). . . . . . . 230
.5 The SEI model of the ‘non-DAC case’. . . . . . . . . . . . . . . . . . . . . . 231
List of Figures 21
.6 Full displays of Fourier spectral analysis for Hen 2-138: above He i λ 4026
(l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r). . . . . . . . . . . . 233
.7 Full displays of Fourier spectral analysis for Hen 2-131: above He i λ 4026
(l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r). . . . . . . . . . . . 234
.8 Full displays of Fourier spectral analysis for NGC 2392: above He i λ 4026
(l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r). . . . . . . . . . . . 235
List of Tables
3.1 Preliminary parameters for NGC 6543 . . . . . . . . . . . . . . . . . . . . . 83
3.2 UV/FUV ion species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3 FUSE channels & FUV spectral sections . . . . . . . . . . . . . . . . . . . . 88
3.4 NGC 6543 F034 observations . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.5 NGC 6543 F034 Mq results . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.6 Comparison of NGC 6543 and mid O-star properties . . . . . . . . . . . . . 112
4.1 FUSE objects – details of observations . . . . . . . . . . . . . . . . . . . . . 121
4.2 FUSE objects – central star parameters . . . . . . . . . . . . . . . . . . . . 124
4.3 FUSE objects average mass-loss-ionisation fractions . . . . . . . . . . . . . 137
4.4 NGC 6826 P v DAC progress . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.5 IC 2149 P v DAC progress . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.6 FUSE objects’ P v equivalent width measurements . . . . . . . . . . . . . . 157
4.7 FUSE objects’ P v TVS (approximate) variability ranges . . . . . . . . . . 157
4.8 FUSE objects’ P v DAC migration . . . . . . . . . . . . . . . . . . . . . . . 158
5.1 Hen 2-138 central star parameters . . . . . . . . . . . . . . . . . . . . . . . 164
5.2 Hen 2-131 & NGC 2392 central stars’ parameters . . . . . . . . . . . . . . . 166
5.3 ESO 3.6 m & HARPS specifications . . . . . . . . . . . . . . . . . . . . . . 167
5.4 ESO La Silla observation log summary. . . . . . . . . . . . . . . . . . . . . 168
5.5 SEI-derived mass-loss and wind ionisation parameters . . . . . . . . . . . . 172
5.6 Hen 2-138 equivalent width measurements . . . . . . . . . . . . . . . . . . . 190
5.7 Hen 2-131 equivalent width measurements . . . . . . . . . . . . . . . . . . . 191
5.8 NGC 2392 equivalent width measurements . . . . . . . . . . . . . . . . . . . 191
5.9 Hen 2-138 TVS velocity ranges . . . . . . . . . . . . . . . . . . . . . . . . . 193
22
List of Tables 23
5.10 Hen 2-131 TVS velocity ranges . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.11 NGC 2392 TVS velocity ranges . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.12 Hen 2-138: Fourier power spectra peak frequencies . . . . . . . . . . . . . . 195
5.13 Hen 2-131: Fourier power spectra peak frequencies . . . . . . . . . . . . . . 197
5.14 NGC 2392: Fourier power spectra peak frequencies . . . . . . . . . . . . . . 207
Chapter 1
Introduction
1.1 Introduction to Planetary Nebulae
For a low-mass Dwarf Star – luminosity class V – for which M⋆ ∼ 3M⊙, during its main
sequence core hydrogen-burning phase, the mass-loss incurred is of little significance to
its evolution, being only of the order of only 10−12 M⊙ yr−1; and with a main sequence
lifetime of approximately 400 million years (4 × 108 years), the amount of mass lost is
negligible.
When core H-burning ceases but continues in a H-burning shell surrounding the inert
core, the outer envelope, heated by the burning H-shell, expands and cools and the sub-
sequent appearance of a temperature gradient within the envelope sets up a convective
zone which extends as far down as the region where the products of the core burning are
present, and so starts to ‘dredge’ the H-burning products from the core to the surface;
and when the envelope is fully convective, the star enters the so-called Red Giant Branch
(RGB) – luminosity class III – upon the Hertzsprung-Russell Diagram (HRD).
When the inert core, now shrunken and degenerate (where the pressure inside is in-
dependent of temperature), has reached a high enough temperature to remove the degen-
eracy through the helium core flash, core He-burning commences, the core expands and
the swollen envelope shrinks – the star then enters upon the horizontal branch of the HR
diagram.
When core helium-burning is exhausted, the star continues to burn helium in a shell
24
1.1. Introduction to Planetary Nebulae 25
around the now carbon core (in a similar manner as the hydrogen burning shell around the
formerly helium core, following the main sequence). The H-burning shell continues; and so
the star now enters upon a double shell-burning phase, where 10% of the star’s luminosity
is generated from the inner He-burning shell surrounding the inert carbon core, and 90% if
generated by the outer H-burning shell surrounding the inert helium zone between the two
burning shells. Again the inert core starts to shrink and once again become degenerate;
again the burning shells expand the star’s outer envelope, but to radius approximately 10
times that of the former red giant stage; it now moves onto the Asymptotic Giant Branch
(AGB) – also luminosity class III. Another temperature gradient establishes itself and so,
once again, the envelope becomes deeply – almost completely – convective, dredging up
the material created by the H-burning shell. While in the AGB phase, the star’s further
evolution is now completely dominated by mass-loss.
The He-burning shell continues to dump fresh (carbon) material upon the inert core,
thereby increasing its mass, and with increasing mass so the star’s luminosity increases
and moves up the AGB; the mass-loss rate increases tremendously from about 10−9 to
about 10−5 M⊙ yr−1 at the ‘tip’ of the AGB.
The increased mass-loss rate coincides with the onset of thermal pulses: after it has
burned outward for some time, the H-burning shell cools and ‘switches off’; the He-shell
continues to burn and so likewise moves outward in mass until it reaches the H-rich layers;
and as this material meets the 108 K He-burning shell, it is re-ignited – producing a
thermal pulse in the star, and as a result of which, the star once again experiences a
double shell-burning.
Once again the H-burning shell moves outwards, cools, and is subsequently extin-
guished; and the whole process, culminating in a thermal pulse, repeats, and continues to
do so with a period of approximately 104 years, during the AGB phase. The instability
results in a third and final convection-based ‘dredge-up’, enabling the products of the
He-burning shell, namely carbon and possibly oxygen, to reach the surface.
The mass of the convective envelope decreases due to two co-existing processes: in-
wardly, the shell-burning process continue to add mass to the inert core; and also out-
wardly, the stellar wind mass-loss continually removes material from the outer envelope.
During the AGB phase the effective temperature of the star is of the order of Teff ≃3000 K, so the radius scales as R⋆ ∼ L⋆
0.5. As the luminosity increases exponentially, the
mass-loss rate increases almost exponentially. With L⋆ = 104 L⊙, R⋆ = 400 R⊙ and M⋆ ≃
1.1. Introduction to Planetary Nebulae 26
M⊙, this gives a mass-loss rate of around 4 ×10−6 M⊙ yr−1.
When the mass of the envelope has reached a minimum value of around 10−3 M⊙,
there is now not enough (envelope) material to be able to sustain the convection within;
and so the envelope starts to contract into radiative equilibrium. The star then moves to
the left on the HRD as the AGB phase comes to an end. It can be shown that for a star
of initial mass 3 M⊙ the core mass at the end of the AGB is 0.64 M⊙ – almost equal to
the star’s entire mass by this stage – this of course depends upon the amount of mass lost
thus far.
Once the star has left the AGB, it contracts and moves to the left in around 104 years,
with little (vertical) change of luminosity; and as the core mass hardly changes during
this time, the luminosity remains constant, and so the leftward move is horizontal upon
the H-R diagram. The location of the star along this line is therefore determined by the
mass of the envelope. The very small envelope mass decreases steadily because the fusion
taking place within shells (H & He) removes material from the envelop and dumps it upon
the core; and also because of a stellar wind – now of the order of 10−9M⊙ yr−1 during this
phase. When the envelope mass has reduced to about 10−4M⊙ the star has an effective
temperature of about 30,000 K . In actual fact the time it takes for the star to move across
this post-AGB line on the HRD – the ‘crossing time’ – is determined by how long it take
for the star’s effective temperature to rise from about Teff ≃ 3000 K to about Teff ≃ 30,000
K. Once at this high temperature the star, now with a radius R⋆ ≃ 4R⊙ will develop a
line-driven wind with a mass-loss rate of 10−9 to 10−7M⊙ yr−1 and a velocity of around
1000 km s−1. This fast line-driven wind will overtake the slow dust-driven wind of v∞≃ 10
km s−1 from the AGB phase, and the two will interact to produce a planetary nebula. The
remaining star – now really just the inert core – is now the central star of the planetary
nebula.
The central star producing the significantly radiatively-driven wind mass-loss of around
10−9 to 10−7M⊙ yr−1 will reduce the envelope mass to a even lower value; and when the
envelope mass becomes too low, Menv < 10−5M⊙, shell-burning will stop, and the central
star will cool down and transform into a degenerate White Dwarf – luminosity class VII.
The white dwarf’s mass is almost equal to that of the mass of the star’s core as it
left the AGB, with only a slight increase in mass as it crossed the HRD. The mass of the
white dwarf is 0.64M⊙, whereas the initial mass of the star was 3M⊙ – so the star has lost
2.36M⊙.
1.1. Introduction to Planetary Nebulae 27
White dwarf masses are typically between 0.5 and 0.7M⊙, and stars with an initial
ZAMS (zero age main sequence) mass of up to 8M⊙ can eventually form white dwarfs; so
these stars must have lost a significant proportion of their mass over their evolutionary
lifetime in the form of a stellar wind.
1.1.1 Hydrogen-rich CSPNs
In this thesis the focus will be on spectral Of-type hydrogen rich CSPNs: those which ex-
hibit strong hydrogen lines (in absorption and emission) in their spectra; and are therefore
often called O-type, as this higher level of spectral hydrogen in analogous to that of hot
OB-type stars. The Of-type CSPN is therefore categorically separate from the hydrogen-
deficient Wolf-Rayet (WR-type) CSPNs, whose central stars exhibit a hydrogen-depleted
core, thereby revealing the helium-rich layers, the spectra of which therefore show strong
absorption and emission lines in helium particularly.
1.1
.In
troductio
nto
Pla
neta
ryN
ebula
e28
Fig. 1.1. Diagram of stellar evolution of a solar mass star from the main sequence to a white dwarf, courtesy of R.K. Prinja(via private communication).
1.2. The Introduction of Stellar Winds 29
1.2 The Introduction of Stellar Winds
A stellar wind is the term which was first ascribed by Eugene Parker in 1960 to the outflow
of material from the surface of a star, for as well as radiation, a star emits particles. It is
the both the rate at which the material flows out, and the structural form of this material
which is of tremendous importance in the way in which the star evolves through the latter
stages of its life; and indeed, its ultimate end is determined by the rate at which this
‘wind-blown’ material is lost.
In 1600, the astronomer Blaeu discovered a ‘new star’, or ‘nova’; but unlike those stars
so named today, which catastrophically end their lives in supernovae explosions, Blaeu’s
‘nova’ is merely a star with a very strong but steady stellar wind. This star became
known as P Cygni, and in the nineteenth century optical prism-based observations of
other stars also showed stellar line profiles similar to those noted within the spectra of
P Cygni: these profiles possess a blue-shifted absorption component and a red-shifted
emission component, and such line profiles have proven to be key diagnostic tools when
investigating the physical properties of stellar winds.
1.2.1 The Observation of Stellar Winds
It is the emission of particles from a star that is given the semi-misnomic appellation of
a stellar wind. This emanation of material from the surface of the star can be described
using the parameters of mass-loss rate – the amount of mass lost by a star per unit time
– and the wind’s terminal velocity – the speed the wind approaches at a relatively infinite
distance from the star.
Mass-loss is conventionally described in units of solar masses (lost) per year i.e M⊙ yr−1 =
6.303×1022 kg s−1 with typical values in the order of M = 10−6M⊙ yr−1 or the equivalent
loss of mass equal to the mass of the Earth every three years; a star’s terminal velocity can
range from a little as 10 km s−1 for a cool supergiant to around 3000 km s−1 for a luminous
hot star.
In it simplest model form, a star with a stationary spherically symmetric wind expe-
riences a mass-loss rate which is related to its density and velocity at any radial point in
the wind via the equation of mass continuity :
1.2. The Introduction of Stellar Winds 30
M = 4πr2ρ(r)v(r) (1.1)
where r is the (radial) distance from the star’s centre, ρ is its density, and v its velocity.
The equation states that the same amount of gas flows per second through a sphere of
radius r from the centre of the star – and therefore no material is created or destroyed in
the wind.
Gas escaping for the photospheric surface of the star is accelerated outward – initially
by radiation pressure – from a small radial velocity v ≤ 1km s−1 at the photosphere to
a much higher velocity at a great distance from the star – it eventually asymptotically
approaches a terminal velocity v∞ = v(r → ∞).
The wind’s velocity distribution at a distance r from the star is given by a velocity
law v(r) which is itself governed by a β-law which shows the rate of variation of the
distribution:
v(r) ≃ v0 + (v∞ − v0)
(
1 − R⋆
r
)β
(1.2)
This shows the increase of v with distance r from the star, from v0 at the surface to
v∞ at great distance, with v0 > v∞. The β-factor describes the steepness of the increasing
velocity curve.
By introducing relative variables, w = v/v∞ and x = r/R⋆, the above velocity law
becomes parametrised thus:
w ≃ w0 + (1 − w0)
(
1 − 1
x
)β
(1.3)
It is this standard form which will be used within the Sobolev with Exact Integration
(SEI) stellar wind modelling process in later chapters.
1.3. The Formation of Spectral Lines 31
1.3 The Formation of Spectral Lines
Spectral lines found within stellar winds are easily distinguishable from photospheric lines
due to their larger width and wavelength shift; they can be formed via photon absorption,
emission, or a combination of the two processes: a P Cygni profile.
1.3.1 Line scattering
A photon emitted by the photosphere can be absorbed by an by an atom and an electron
excited to a higher energy level. After a short time the electron can subsequently return
through de-excitation to its original level, re-emitting a photon with almost a similar
energy to that of the initial, the only difference in energy due to the Doppler shift owing
to the thermal motions of the atom. As the photon is only altered upon emission in terms of
its direction of travel this process is referred to as line scattering. If the electron is excited
from its ground state then the line transition is referred to as a resonance transition and
the scattering is specifically called resonance scattering – this is the process that results
in the formation of a P-Cygni line profile.
1.3.2 Line emission by recombination
An ion within the stellar wind can encounter an electron and recombine with it, with the
most likely recombination being back down to the ground state of the atom. It is also
possible however for the atom and electron to recombine to a higher, excited state. The
electron may then drop down from higher to lower energy states emitting line photons into
the stellar wind at each stage of its cascade through photo-de-excitation. Lines formed
through specific transitions that have a high probability of being produced via photo-de-
excitation will then be seen in emission, such as the Hα and infra-red lines in hot star
winds.
1.3.3 Line emission for collisional- or photo-excitation
Atomic excitations from the ground state to an excited state can also occur via collisions
where kinetic energy is converted, via the initial excitation and subsequent photo-de-
excitation to a lower level, into photon energy.
1.4. P Cygni Profiles 32
1.3.4 Pure absorption
Photo-excitation of an electron from a lower energy level to a higher one can be followed
by spontaneous de-excitation to another lower level, whereby the initial transition photon
is destroyed and new photons created by the second transition. However this is not a
major occurrence in stellar winds as the majority of atoms in the stellar wind are in their
ground state.
1.3.5 Masering by stimulated emission
If a photon travelling through a stellar wind can hit an excited atom or molecule that
can emit a similar photon through photon-de-excitation then the process of stimulated
emission becomes an important factor. The atom (electron) de-excites to a lower level
by emitting a photon with the same frequency and in exactly the same direction as the
original photon. So now there will be two similar photons travelling in the same direction,
and if this process is repeated the result will be large numbers of line photons travelling
in the same direction a process called masering. In order to be a significant source of
photon emission a large number of atoms/molecules have to be in an excited ‘upper level
of transition’ and there should not be a velocity gradient present in the direction of the
travelling photons - if there was, then the Doppler shift will curtail this process.
This process is responsible for the very strong and very narrow maser emission lines
of abundant molecules in the winds of cool stars.
1.4 P Cygni Profiles
Spectral lines caused by atomic transitions/excitation of electrons from the ground state
to higher states – called resonance lines – offer the most sensitive indicators of mass-loss.
In the ultraviolet (UV) the most common are the resonance lines of C iv , Nv , and Si iv .
There is a large abundance of these ions, and with the the large oscillator strength
of their atomic resonance transitions they can show an observable line absorption that
exhibits Doppler shift due to the outflow – even if the rate of mass-loss is small.
For a column density of between 1013 to 1014 ions cm−2, the resonance lines produce
a small but significant (i.e. weak but observable) absorption component which is subse-
quently Doppler shifted to a shorter wavelength because it is formed in a region that is
moving outward from the star i.e. towards the observer.
1.4. P Cygni Profiles 33
Fig. 1.2. Diagram of components of a UV P Cygni resonance line profile: Lamers& Cassinelli (1999)
But if the column density is in the region of 1015 ions cm−2 then a P Cygni profile is
formed, with a blue-shifted absorption component and a red-shifted emission component.
1.4.1 The Formation of P Cygni Profiles
The manner in which a P Cygni profile is formed is best explained using a model of a
spherically symmetric star with a similarly-spherical outflowing wind in which the velocity
increases as the wind travels outwards.
Four regions contribute to the observed profile:
• S: the star emitting a continuum - with a photospheric absorption component at the
rest wavelength, λ0, of the line.
1.5. Mass-Loss Studies from P Cygni Profiles 34
• F: the ‘tube’, the region of outflow in front of the stellar disk. The gas in F is moving
towards the observer with velocities ranging between v0 and v∞.
• O: the ‘tube’, the region of outflow occulted by the stellar disk. Gas is moving away
from the observer; radiation from this region does not reach the observer.
• H: the regions to the sides of the star that would be observed as a halo – if the wind
could be resolved spatially by the observer. The gas in the region has both positive and
negative velocity components along the line of sight of the observer.
Figure 1.2 shows how the spectral contributions from all the different regions go toward
producing a P Cygni profile.
1.5 Mass-Loss Studies from P Cygni Profiles
Spectroscopic studies have been carried out using P Cygni resonance line profiles, particu-
larly UV resonance lines found within the spectra of early-type stars, whence information
about the mass-loss involved and wind profile information has been obtained (Lamers &
Cassinelli 1999). The profiles of strongly saturated resonance lines are strongly sensitive
to the velocity law, and subsequently an accurate estimation of the wind terminal velocity
can be obtained from the position of the very steep blueward edge of the absorption line
which reaches the continuum at a Doppler velocity of vedge ≃ −(v∞ + 2vturb), where vturb
is the turbulent velocity in the wind at a distance of r & 10R⋆ where the wind reaches
its terminal velocity, v∞. Whereas the terminal velocity can be directly measured from a
saturated resonance line, unsaturated lines are used to derive the mass-loss rate.
Observed profiles are compared to predicted profiles of different radial positions ni(r)
of the observed ions in the wind, and when the observed and predicted profiles match,
then the distribution of ni(r) is known. Using the ion density ni(r) can be converted into
a density distribution ρ(r) using the abundance and the ionisation fraction of the observed
ion is known in the wind:
ni =ni(r)
nE(r)
nE(r)
nH(r)
nE(r)
ρ(r)ρ(r) = qi(r)AE
nH
ρ
M
4πr2v(r)(1.4)
where AE = nE/nH is the abundance of element E with respect to H and qi = ni/nE
is the fraction of ions in the right stage of ionisation and excitation to produce the line.
The ratio nh/ρ depends on the composition of the wind and is (1.36mH )−1 = 4.43 × 1023
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 35
atoms g−1 for solar composition. The mass continuity equation here gives ρ in terms of
M , so that if v(r) and ρ(r) are known then the mass-loss rate and the wind’s terminal
velocity – as well as the wind’s velocity law in – can be derived from P-Cygni resonance
profiles.
1.6 Spectroscopic Investigations into Central Stars of Plan-
etary Nebulae
Studies of stellar winds & mass-loss have been extended from OB stars to hydrogen-rich
O-type CSPNs and observational data has been analysed with a view to compare the
mechanisms and subsequently derived parameters from both, and to see if the two types
of stars have a common relation between their luminosity and their mass-loss through
their stellar winds.
UV spectra of CSPNs show P Cygni profiles in ions C iv , Nv , and Si iv , and some-
times lines from excited levels of N iv , O iv , and O v . The high effective tempera-
tures of these stars is between 30,000 K and 120,000 K and their luminosities range
between 3.5 < log L⋆/L⊙ < 4.3. This implies a radii of about 0.3 to 3 R⊙ – from
L⋆/L⊙ = 4π(R⋆/R⊙)2σ(T⋆/T⊙)4. Masses are small and of the order 0.5 to 0.6 M⊙ because
they are the progenitors of white dwarfs. The combination of low mass, small radii and
high luminosities implies that the effective escape velocity at the stellar surface is between
200 and 800 km s−1.
Mass-loss rates for CSPNs have been derived from the P Cygni profiles of UV lines,
and from optical emission lines (see Mendez et al. 1992; Perinotto 1993; Kudritzki et al.
1997). Mass-loss rates are small and of the order of 10−9 to 10−7 M⊙ yr−1, however these
low mass-loss rates provide strong P Cygni profiles because the stars’ radii are so small.
The optical depth of the P Cygni profiles scale roughly with the column density in the
wind and inversely with the terminal velocity, so τ ∼ M /(R⋆v2∞). A typical CSPN with
M = 10−8M⊙ yr−1, v∞ = 3000 km s−1 and R⋆ = R⊙, will have approximately the same
optical depth of the P Cygni profiles as a typical O supergiant of R⋆ = 50 R⊙ with v∞ =
2000 km s−1 and M = 2 × 10−5M⊙ yr−1.
Much of the diagnostic work carried out upon stellar wind spectra has centred upon
the creation of plane-parallel nLTE model atmospheres and their comparison with the
observational equivalent, which has led to the determination of parameters such as effective
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 36
temperature, surface gravity, and chemical/helium abundance. The establishment of such
parameters, and the consequential attribution of a key position upon the log Teff – log g
plane and the spectroscopic determination of temperature and gravity, has subsequently
aided in the estimation of stellar luminosities, masses, radii and distances when compared
with post-AGB predictions and the core mass - luminosity relationship.
According to stellar theory, stars close to the Eddington limit in the log g – log Teff
diagram should show signs of an active radiatively-driven wind, and successful theory
should be able to quantitatively reproduce wind conditions to those observed in CSPNs – in
a similar fashion to the hitherto successful reproduction of winds observed from O, B, and
A stars (Kudritzki et al. 1997); also the radiatively-driven wind theory predicts – assuming
solar abundances – that a relationship exists between the mass-loss - terminal velocity
product, M v∞, having dimensions of momentum-loss rate, and the stellar luminosity:
M v∞ ∼ R−0.5⋆ L
(1/α)⋆ (1.5)
where α is the power law exponent of the line strength distribution function and has a
value ≃ 2/3 (Kudritzki et al. 1995; Puls et al. 1996). Hence the stellar momentum-loss
rate and luminosity are proportionally-related thus:
M v∞R0.5⋆ ∼ L
(1/α)⋆ (1.6)
A plot of log M v∞R⋆0.5 against log L⋆ shows – in the first approximation – a linear
relationship which is followed by massive hot stars of solar abundances, see Figure 1.3.
It was found that the CSPNs studied and analysed with the fitting of the Hα lines
fitted the straight line plot, although there was a split between the two groups – with
the implication that some of the CSPNs possessed a strong stellar wind, whereas others
were weaker – as shown in Figure 1.3. A similar diversity of wind strengths had been
found in massive hot stars but this was attributed to a difference in relative metallicities
between the two sub-groups: the hot stars of the SMC had a lower average metallicity and
a weaker wind than those found in the LMC or the galaxy. However, at the time little
was known about the metallicities of CSPNs and so no metallicity-dependent comparisons
could be drawn, but there existed a motivation to investigate the UV spectral lines e.g
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 37
Fig. 1.3. The log of the quantity M v∞R⋆0.5 as a function of the log of stellar
luminosity for a selection of hot stars: open triangles, squares, and diamondsindicate O, B and A supergiants; asterisks indicate lower luminosity class O stars(giants to main sequence stars). Plus signs are for CSPNs. The straight line is theindicator of the relation following the 3/2 power of stellar luminosity: Kudritzkiet al. (1997).
the abundant Ni and Fe lines. Another consideration as a possible cause of the diversity
was the luminosity class of the progenitor of the CSPN, as the lower-classed hot stars.
The modelling methods used also predicted high masses and luminosities which were
not expected: some are comparable to some of the masses derived in earlier hydrostatic
models by Mendez et al. (1988), where it was expected that they would be closer to
masses as predicted by the later models of Mendez et al. (1992); the highest luminosities
of Kudritzki et al. (1997) contradict the theoretical post-AGB evolution where such high
mass objects should possess far lower luminosities akin to the tracks marked out by cooling
white dwarfs.
Unfortunately high luminosities were needed in order to position the CSPNs into such
an agreeable place upon the momentum loss rate – luminosity diagram, and reducing the
luminosities, as well as the mass-loss rates and radii, the CSPN winds would be strong
enough to move the objects above the line-fit – the winds’ strengths seemingly proven
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 38
higher than the radiatively-driven wind theory could account for. Perhaps there was some
as yet unaccounted for aspect within the wind which would allow for this?
Early plane-parallel-based model fitting of H and He lines of CSPNs was only useful
in predicting values for surface temperature, He abundance and log g, and not useful in
deriving stellar luminosities or masses, but only L/M ratios; and the lack of distance data
of CSPNs could not solve this problem (Pauldrach et al. 2003). Therefore the positions of
CSPNs were plotted upon the log g – log Teff diagram and compared with plots of post-
AGB tracks derived from the log L – log Teff diagram. It was then possible to return to the
former diagram and read off the CSPN stellar mass, from which the luminosity could be
derived; and with a knowledge of the de-reddened stellar magnitude, one could calculate a
so-called ‘spectroscopic distance’ – all assuming that the stellar evolution models provide
an accurate relation between stellar mass and luminosity.
Hydrodynamic Modelling: A Different Approach
An alternative method (Pauldrach et al. 2003) is based upon a homogeneous, stationery,
extended, outflowing, spherically symmetric atmosphere for which the hydrodynamic and
the radiative transfer and rate equations for a nLTE have to be solved: the calculations
for which are performed iteratively, as described briefly below (and in greater detail by
Pauldrach et al. 2001).
An initial estimate for Teff is assumed from a preliminary study of a given star’s visual
or UV spectrum; the latter will also provide a measure of the wind’s terminal velocity,
v∞. An initial value for the stellar radius R, for the Rosseland optical depth, of 2/3 is
submitted. From the theory of radiatively driven winds, where v∞ scales with√
M/R,
the current values of R and v∞ will lead to an estimate of the stellar mass. With (an
assumed set of abundances and) these values of R, Teff , M , the model stellar atmosphere
is solved, with the velocity field, the mass-loss rate. The synthetic spectrum which is sub-
sequently produced is compared with an observed one and the accuracy of the resulting fit
is considered. If the fit is less than satisfactory then the mass-loss rate, M, is re-calculated
with a new value for R (as the radiatively-driven wind theory states that log M ∼ log L).
However, in order to keep a consistent value of v∞ – one that will still match the ob-
served/derived value – the stellar mass has also to be adjusted along with the change in
radius. The modelling process is then repeated and the match of the model wind profile
to the observed one is again considered; and so on, with each iteration moving the model
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 39
closer to the observed wind.
This iterative procedure was successful in modelling the wind of massive Population I
stars such as the supergiant α Cam (HD 30614), and so the aim was to apply a similar
procedure to UV spectra of CSPNs as a means by which to verify whether CSPNs followed
the wind-momentum-luminosity relationship as forwarded by Kudritzki et al. (1997).
The problem lay in the apparent establishment of two sub-groups of CSPNs, lying
above and below the M v∞R⋆0.5 – L⋆ relationship line, with the two groups having either
stronger or weaker winds for their given luminosities. Furthermore, some of the predicted
stellar CSPN masses were high (M > 0.8M⊙), a contradiction of theoretical post-AGB
evolutionary speeds.
Using the hydrostatic models, the terminal velocities and mass-loss rates for the similar
selection of CSPNs were calculated following the current theoretical post-AGB tracks,
and the resulting wind momenta plotted upon the wind-momenta-luminosity diagram. As
with the earlier prediction, the CSPNs do follow the expected wind-momentum-luminosity
relation, but these models (Pauldrach et al. 2003) form a smaller tighter group that those
CSPNs produced by Kudritzki et al. (1997); also the resulting stellar masses have a lesser
spread, between 0.6 and 0.95 M⊙.
Conflicting Results from Terminal Velocities & Mass-Loss Rates
To try and understand the problem, the relations of v∞and Mwere studied separately.
An odd discrepancy is immediately apparent: the measures of v∞ cluster about the
evolutionary tracks for masses between 0.5 and 0.6 M⊙, but on the other hand, the mass-
loss rate measurements are so placed for stellar masses above 0.7 M⊙. When considering
individual CSPNs these discrepancies between implied stellar masses are even wider. For
Hen 2-131, v∞ predicts a mass of 0.6 M⊙, but its M is not compatible with its v∞, and
instead indicates a mass of 0.94 M⊙; for NGC 2392, v∞ predicts a mass of 0.9 M⊙, but
its M is too small for this mass, and would rather indicate a mass of nearer 0.6 M⊙.
In order to try to resolve these difficulties, Pauldrach et al. (2003) turned to the
modelling of UV spectra. An initial UV spectrum modelled for Hen 2-131 for a stellar
mass of 0.6 M⊙ clearly demonstrates that this is too low a mass-loss rate as the spectrum
contains almost only photospheric lines and shows little impact of a wind, which indicates
that the luminosity is too low and needs to be much higher, as it is this which will affect
the mass-loss rate. To correct this, a series of spectra, each calculated with a different
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 40
luminosity, were produced, each time also adjusting the mass so that the wind terminal
velocity remained the same; and the best overall fit was a spectrum giving the required
mass-loss rate as that previously predicted.
For NGC 2392, the problem appeared in reverse: the UV spectrum was dominated by
many wind-contaminated lines which were not evident in the observed spectrum, which
is mainly dominated by photospheric lines. Here, the luminosity is too high, leading to
a mass-loss rate far higher than is the case. A lower luminosity and lower mass-loss rate
produces a spectrum which shows a much better fit to the observed UV spectrum.
NGC 2392: Teff is determined from the ionisation equilibrium of Fe ions in the stellar
UV spectrum – not too different from that derived from the ionisation equilibrium of He i
and He ii absorption lines in the optical spectrum. The low terminal velocity from direct
measurement and the luminosity, decreased from earlier assumption to provide a model
that fits the observed spectrum, have both led to a smaller radius, 1.5R⊙, and v∞ of 400
km s−1; these lead to a stellar mass of 0.41M⊙, which is a much smaller value than that
arrived at via the assumption of post-AGB mass-luminosity relation as used by Kudritzki
et al. (1997), who thus calculated a stellar mass of 0.9M⊙.
Hen 2-131: Teff of 33 kK and the measured v∞ of 500 km s−1 and the higher luminosity
than that suggested by the post-AGB mass-luminosity relation (with which Kudritzki
et al. 1997 derived a stellar mass of 0.9 M⊙) has, with a increased stellar radius in order
to increase M to thereby achieve a satisfactory fit, resulted in a stellar mass of 1.39 M⊙,
which is extremely closer to the Chandrasekhar level above which a type Ia supernova can
result.
These results – particularly the wide range of derived stellar masses, between 0.4 and
1.4 M⊙– evidently do not agree with predictions set by the post-AGB mass-luminosity rela-
tionship. However, when the UV spectra-based results are added to the wind-momentum-
luminosity diagram for hot stars and CSPNs, they possess a tighter dispersion along the
extrapolation of the wind-momentum-luminosity relation as defined for massive hot stars
– see Figure 1.4. This has been due to fitting stellar parameters to UV spectra via modern
hydrodynamically consistent models.
Pauldrach et al. (2004) used the theory of radiative driven winds in an alternative way
by looking at the dependence of mass-loss rates and terminal velocities on stellar lumi-
nosities and stellar mass, and developed a method devised by Kudritzki & Puls (2000)
to determine stellar masses and luminosities from observed/measured wind terminal ve-
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 41
Fig. 1.4. The wind-momentum-luminosity relation for massive O stars andCSPNs. Data is derived from Hα analysis (Puls et al. 1996) – P96; similarfor CSPNs (Kudritzki et al. 1997) – K97. Additionally plotted are the wind mo-menta for O stars and CSPNs based upon the hydrodynamic models followingpost-AGB evolutionary tracks: Pauldrach et al. (2003).
locities and UV mass-loss rates. Applying these techniques to the same select CSPNs as
had been analysed by Kudritzki et al. (1997), they obtained very similar values for Teff ,
but very different values for mass and/or luminosity. Which of the two approaches: the
post-AGB core mass-luminosity relationship used by Kudritzki et al. (1997), or the stellar
wind-based hydrodynamics of Pauldrach et al. (2003), could be proven the more accurate
method? If the latter study was the more physically-sound method to use, then that would
have further repercussions for theory of post-AGB evolution. However, the hydrodynamic
study was based upon a stationary, smooth homogeneous wind, which more recent study
has cast as a false assumption.
1.6.1 Further Considerations of Wind-born Metal Lines & the Contri-
bution of ‘Clumping’.
The primary indication was that winds are radiatively-driven – it is difficult to explain the
stronger wind-momentum-luminosity relation with any other dominant wind mechanism;
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 42
and despite the same model atmospheres working well enough for the massive hot stars,
the spread in the CSPN masses was still a mystery that needed explaining.
The previous models, although based upon nLTE, did not take into account metal line
opacities nor the presence/action of a stellar wind upon the circumstellar nebula, and so
UV spectra of CSPNs, available from IUE, HST and FUSE, and containing many P Cygni
absorption profiles, were now used to determine terminal velocities for the wind as well as
the stellar mass-loss rate.
The appearance of thousand of photospheric metal lines offered a source for determin-
ing the metallicity of the CSPN, and provide a alternative source from which to determine
Teff and through the ionisation equilibrium, for example, of Fe iv /Fe v : e.g. Pauldrach
et al. (2004) and Herald & Bianchi (2004), whose work on this confirmed the earlier
optically-derived temperatures of Mendez et al. (1988) and Kudritzki et al. (1997).
The inclusion of the opacities of millions of metal lines in nLTE with optical spectra
would have two effects: firstly, absorption by strong metal lines in the outer atmosphere
causes a change in the spectra energy distribution in the UV; secondly, around 50% of the
photons are scattered backwards into the inner atmosphere where they supply an addi-
tional energy input to heat the deeper photosphere. This second warming effect increases
the photospheric emission of the continuum and so affects the ionisation equilibrium such
as He i /He ii which are used to determine Teff . Such ionisation equilibria are shifted to-
wards lower Teff . Also, pressure broadened wind of Balmer lines – used as a diagnostic
for log g – become weaker as the millions of metal lines increase the radiative acceler-
ation grad and as such the effective gravity, geff = g − grad, is decreased, and so higher
gravities are needed to fit the Balmer lines. This effect, in combination with the lowered
Teff , leads to an overall shift in the log g – log Teff plane, which when compared with the
post-AGB evolutionary tracks, leads to a reduction of CSPN masses, radii, luminosities,
and distances.
The effects of nLTE metal line-blanketing were considered by Kudritzki et al. (2006),
while reassessing the former optical study of CSPNs (Kudritzki et al. 1997), with the aim
of making a new comparison with the UV study carried out by Pauldrach et al. (2004).
For this, a more up-to-date nLTE wind-analysis code, FASTWIND (Puls et al. 2005),
was used, modelling the wind by including the effects of nLTE metal line opacities, stellar
winds and stellar extension; but ostensibly using a similar method to that used back in
1997: Teff and He abundance are obtained form a fit to the He i and He ii lines’ ionisation
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 43
equilibrium; gravity (log g) is obtained from a fit of the Balmer lines, and as Hα is the
strongest hydrogen line formed in the stellar wind then this is used to gauge the stellar
mass-loss rate. As usual, P Cygni lines are used as a measure for the wind’s terminal
velocity, v∞.
Hα , used as a diagnostic tool for mass-loss rates can be affected by stellar wind
clumping.
It had been well documented that line driven winds are unstable (see Owocki et al.
1988), which might lead to inhomogeneity within the wind, commonly known as clumping
(as described by Runacres & Owocki (2002)), where there are regions within the wind,
the clumps, which possess a higher density, ρcl, and also appositely, regions which are
much less dense. The clumping density is related to the mean density of the wind by a
simply clumping factor, fcl, such that ρcl = ρavfcl – there is a similar relationship with
the clumping factor and the occupation numbers ni of ions.
Line opacities κ depend upon density as κ ∝ ni ∝ ρx. For optically thin clumps
the average optical line depth is given τav ∝ navi ∝ ncl
i f−1 ∝ ρxavf
x−1. For a dominant
ionisation stage x = 1, and so the clumping along the line of sight cancels (f0 = 1) and
does not affect the diagnostics.
There are challenges in deriving the clumping diagnostics for CSPNs, as the density
dependence exponent x will be different for different ions. WR-type CSPNs have very
dense winds and strong wind emission lines and incoherent line scattering produces wide
emission wings, the strength of which goes with x ∼ 1. O-type CSPNs have much less
dense winds and so this technique is unworkable. The UV P Cygni profiles of dominant
ions tend to be saturated and so the ionisation equilibria become uncertain. However
recent work with massive O-stars using FUSE spectra have used the P v resonance lines
1118 and 1128 A, as having a low cosmic abundance: these lines are un-saturated even
when in the dominant ion stage, and significant clumping has been found (Hillier et al.
2003; Bouret et al. 2005; Fullerton et al. 2006b).
1.6.2 FUSE & the Contribution of UV Resonance Line Modelling
In attempting to gain an understanding of the mass-loss rate of a given star, there are
certain key diagnostics to look for: 1. free-free continuum emission in the radio wavelength
range, located in the rarefied outer edge of the stellar atmosphere; 2. Hα line emission,
detected in the dense and rapidly accelerating region close to the star; and then 3. UV
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 44
resonance-line absorption, found between the two other extremes. The physical mechanics
behind these diagnostics also differ in their dependency on local conditions: emission ∝ ρ2;
absorption ∝ ρ.
The main problem in attempting to gain reliable information about mass-loss rates
from resonance line profiles is that their strength depends upon the radial optical depth
detected at a particular point, i.e:
τrad ∝ M qiAE (1.7)
where AE is the abundance of element E and qi is the ionisation fraction of stage i.
Consequently, this implies that for a dominant ion (qi∼ 1) the mass-loss rate can be
measured directly. However many dominant UV resonance lines are saturated, particularly
those abundant elements, e.g. C, N, O, and so cannot provide reliable values. This usually
leaves elements with only trace ionisation species, where qi . 10−3, used to calculate Mqi
and with little information regarding estimates of qi, there can be little reliability in
prediction of M from such sources. As a result, mass-loss rate estimates have been taken
from measures of free-free radio emission, M (radio), and Hα , M (Hα ) (see Lamers &
Cassinelli 1999; Puls et al. 1996). However, these sources are not without their problems:
radio emission sources are regarded as the most reliable, it is relatively weak, and due
to the ρ2 dependence of the mass-loss rate, the star in question has to be fairly close
by. Alternatively, Hα emission (also ρ2 dependent) can be viewed in distant objects,
but its use depends upon a knowledge of, and the ability to model, the wind-photosphere
interface, which is more difficult.
In recent years, access to data obtained via the Far Ultraviolet Spectroscopic Explorer
satellite (FUSE ) has offered a range of resonance lines in the far-ultraviolet (FUV) – and
as a result, analysis of UV resonance lines has been reviewed and compared with the more
‘traditional’ Hα M (ρ2) measurements of mass-loss. This reassessment of UV resonance
line-based mass-loss estimations is based upon work carried out upon the Pv λλ 1118, 1128
doublet: important because the lines, despite the high ionic abundance, are unsaturated
as the cosmic abundance of P is low. Also, unlike C, N, and O, P is not a product of
hydrogen-burning and so its abundance is little changed over the lifetime of a star, so
differences in abundance from star to star matter little to the general range of mass-loss
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 45
calculations.
A P v -based O star mass-loss survey, conducted by Fullerton et al. (2006a), estab-
lished a strong set of UV resonance line-based density-dependent mass-loss calculations
for comparison with results from both former radio-based and Hα -based ρ2-dependent
mass-loss measurements. The survey is biased toward more luminous O stars as all three
mass-loss diagnostics, the two ρ2-dependent and the P v lines, are detected in the denser
outflows of this type of object.
The ratios of M (Hα ) to M (P v ) and M (radio) to M (P v ) were calculated for each
of the stars studied were all much greater than unity, and these deviations can also be
categorised in terms of the spectra classes of the stars:
1. mid O-type stars (O4 - O7.5) with strong wind features (those with log Mq(P v )
≥ -8) show the smallest deviations from the values of M (Hα ) or M (radio).
2. earlier (O2 - O3.5) and latest (O8 - O9.7) O-type stars show larger deviations from
the 1:1 correlation line.
3. The largest deviations belong to a group of five mid O dwarfs and giants that have
M (Hα ) measurements and only upper limits for Mq(P v ).
If q(P4+) approaches unity for a range of O stars then M (P4+) should agree with both
M (radio) and M (Hα ) for a similar range of stars.
There was found to be an overall trend that the resulting measured values for Mq(P4+)
were significantly smaller than M (ρ2) and the deviations do not depend upon whether
the M (ρ2) values are either M (radio) or M (Hα ) . It was noted however that stars of
classes O4 - O7.5 deviated the least and those of classes O2 - O3.5 and O8 - O9.7 deviated
the most.
Mq(P+4; w) =mec
πe2
4πµmH
fijλ0APR⋆v
2∞x2w
dw
dxτrad(w), (1.8)
The Mq(P4+) equation (1.8) shows that Mq(P4+) could be underestimated if either
the oscillator strength, fij, or the abundance of P, AP , is overestimated. As P4+ is lithium-
like, according to Morton (2003), there is no reason to suppose there is any significant
uncertainty with the oscillator strength.
The abundance of P is a little more uncertain: Pauldrach et al. (1994, 2001) have
adopted sub-solar values to achieve good wind profile fits for select stars, but otherwise
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 46
there is little evidence to assume sub-solar P abundances systematically; other studies –
e.g Lebouteiller et al. (2005) – have also argued that P abundance is solar.
The most likely reason for Mq(P4+) being generally underestimated is that its q value
never reaches a dominant level of ∼ 1, however this is not predicted by standard wind
models, but a suggestion of Pauldrach et al. (1994) is that as the ionisation of He ii (54.416
eV; 228 A) seemingly coincides with that of P v (65.023 eV; 191 A), then it is suspected
that the behaviour of q(P4+) might be influenced by that of He ii .
Maybe the production of soft X-rays, which are themselves beyond the standard wind
model, may also have an effect upon the ionisation balance of the wind, but ions with ion-
isation states above (e.g. S5+) and below (e.g P 3+) P4+ shows no signs of overpopulation.
Therefore, in terms of the standard wind model, there is no definitive reason why
measurements of Mq(P4+) should be underestimated by a factor ≤ 10.
1.6.3 Introducing the Concepts of ‘Clumping’
The lack of definite cause for the discrepancies between mass-loss calculations between
differing methods of measurement begs one to question the assumptions inherent within
the standard wind model, particularly the assumption of the apparent smoothness of
the density distribution (Fullerton et al. 2006b). Selected idiosyncrasies noted in the
modelling of winds include: striking variability in UV and Hα profiles (e.g. see Prinja &
Howarth 1986; Kaper et al. 1996; de Jong et al. 2001; Markova et al. 2005); variable blue
wings in saturated absorption profiles of UV resonance lines (Puls et al. 1993); variable
underlying structures seen in emission-lines (Eversberg et al. 1998); and X-rays detected
in stellar winds (Cassinelli et al. 2001) – all factors indicating an apparent instability
inherent in stellar winds, possibly resulting in a redistribution of material into a far more
in-homogeneous wind, subsequently peppered by denser ‘clumps’.
With Hα and radio emission mass-loss calculations dependent upon ρ2 diagnostics
as they are produced from the interaction of two particles, the effect of clumping should
significantly affect such mass-loss measurements; and with subsequently interpretation
after a standard model smooth wind, the ρ2 diagnostic will consequently over-estimate the
true mass flux, as the denser inhomogeneity of the medium (in producing a heightened level
of emission) will be incorrectly supposed to have arisen from a smooth and homogeneously
denser medium.
Clumping is described in a two component model: dense clumps of density ρH sep-
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 47
arated by rarefied inter-clump gas, density ρL – this depicts a redistribution of the gas
material while preserving the overall mean density, ρs
ρs = fρH + (1 − f)ρL = ρH [f + (1 − f)x] (1.9)
where f is the volume filling factor of the denser component, 0 < f ≤ 1, x is the density
contrast, x = ρL/ρH
With a lack of understanding of the precise mechanism which redistributes the material
in the wind into clumps, the above formulae is often simplified by an assumption of the
dense clumps being separated by a vacuum, so that x = 0 and ρs = fρH
In considering the mis-interpretation of ρ2 diagnostics, Abbott et al. (1981) have shown
that the mass-loss, M (ρ2) will be overestimated by a factor:
{
[f + x(1 − f)]2
f + (1 − f)x2
}1/2
(1.10)
So that in the extreme case that x = 0, that is if the clumps were separated by a
vacuum, M is overestimated in the smooth wind model by a factor of 1/√
f , leading to
M (ρ2) c =√
fM (ρ2) s – “c” and “s” for clumped and smooth.
Alternatively, Mq measurements, based upon UV resonance line profiles, are not sim-
ilarly affected by clumping: being based upon the determination of the radial optical
depth of the material associated by a specific ion along the line of sight, resulting in the
formation of the observed P-Cygni absorption trough. Optical depth is an integral quality,
and so Mq measurements are not sensitive to the distribution of material along the line
of sight (Fullerton et al. 2006b). Actually, if the clumps are optically thin on the spatial
scales relevant to the line transfer, then they will not hide any ‘inter-clump’ material and
measurements taken will be reasonably accurate; however, if clumps are optically thick,
then their distribution will essentially create a porous structure in the wind which must
be taken into account.
1.6.4 The Additional Effects of Porosity
Massa et al. (2003) have shown how the porosity in the wind can, in extreme cases,
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 48
produce unsaturated profiles which would otherwise be saturated if the wind were treated
as smooth.
On larger spatial scales, inhomogeneities will be directly observable in the way they
affect the expected shape of P-Cygni profiles – in the wind profiles of O-type star these
have been assigned as discrete absorption components (DACs) – (see Prinja & Howarth
1986; Kaper et al. 1996) – readily modelled by SEI code.
An excellent SEI fit to the P v profiles of HD 190429A (O4 If+) provides a very well
determined Mq(P4+) – Bouret et al. (2005) achieved a similar fit but only for a clumped
model with a P v abundance reduced to P/P⊙ = 0.5, and with this P abundance, their M ,
their mean q(P4+) = 0.5 over the velocity range 100 – 1000 km s−1, the clumped CMFGEN
model predicts log Mq(P4+) = −6.08. In comparison SEI model results scales to their P
abundance (half-solar) gives log Mq(P4+) = −6.06 – this agreement confirms that both
techniques determine the same optical depth in the line when clumping is incorporated in
the models and all other factors are equal i.e. clumping does not bias the determination
of Mq from wind profile fits to UV resonance lines.
In recent years the Chandra X-ray satellite has detected the emission of X-rays emanat-
ing from the atmospheres of hot supergiant stars, in the form of resolved X-ray emission-
line profiles with half-widths of ∼ 1000 km s−1, leading to the idea that these are produced
within the expanding & accelerating stellar wind by the shock/interaction of instabilities
embedded within the stellar outflow (Owocki & Cohen 2006). Also the apparent sym-
metry of the line which is in opposition to the more asymmetric shape as predicted by
the standard wind theory, with ‘traditionally’-derived mass-loss rates – i.e. taken from
measurements of either Hα or free-free radio emission – where bound-free optical depths
are expected to be of the order of 10 (Hillier et al. 1993), and subsequent attenuated
redshifted emission. However, in trying to fit the observed symmetrical emission lines, the
mass-loss rates have had to be reduced by at least a factor of 5: this may be yet another
aspect of the now long held view that ‘standard’ mass-loss rate calculations, based upon
the hitherto standard stellar smooth wind model (ρ2) have led to an overall overestimation
of mass-loss rates, if, as is now strongly suspected, the winds are actually clumped.
An alternative suggestion to clumping as a possible cause of the strange symmetry of
the X-ray emission profiles is the potential effect of porosity of the wind, namely that if
the wind material is compacted into clumps then redshifted X-ray emission might more
readily be transmitted through the relatively low density of the apparent porous spaces
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 49
between the said clumps (Owocki & Cohen 2006).
An important concept when considering the level of porosity of the wind material is
that it can depend on both the scale size of the individual clumps as well as the overall pro-
portion or filling factor of the clumpiness – large porous gaps will arise from a combination
of large clumps combined a relatively low number of such in a given volume.
Emission and absorption that arise from atomic states arise from recombination colli-
sional excitation or free-free processes all depend upon the proximate interaction of two
constituents e.g. ions and electrons, and thus scale with their individual particle (number)
densities i.e. neni which for a fixed ionisation and abundance is simply proportional to the
square of the mass density, ρ2; and so the effect upon spatial structure on such diagnostics
is traditionally accounted for in terms of a simple density-squared clumping correction,
Cc:
Cc ≡< ρ2 > / < ρ >2 (1.11)
In a model medium which is comprised of clumps of mass, mc of scale l separated by
a distance L ≫ l, the mean density is < ρ >= mc/L3 and the individual clump has a
density ρc = mc/l3 =< ρ > /(L/l)3
The clumping correction is simply given by the inverse of the filling factor – the filling
factor given as the ratio between the volume of the individual clump to the volume asso-
ciated with the clump separation i.e. f = l3/L3 – this is different from the filling fraction,
f ′, which is given as f ′ ≡ l3/(l3 + L3) = f/(1 + f), normalised to vary between 0 and 1.
Cc = 1/f ′ (1.12)
For traditional mass-loss rate diagnostics – Balmer or radio emission, proportional to
ρ2 – the associated overestimate is inferred mass-loss rate scales as M ∼ C1/2c ∼ 1/
√f ′
So the density-squared correction factor depends only on the filling factor and not on
the scale of the individual clumps. As long as the emission can escape from the individual
clumps – if they are optically thin – then the correction factor can be applied to a wide
range of structure.
Attenuation of X-rays occurs through bound-free absorption, often from the ground
1.6. Spectroscopic Investigations into Central Stars of Planetary Nebulae 50
state; and as this is the dominant stage of the absorbing ions, there is no interaction with
other particles, so the absorptions scales linearly with density.
The attenuation per unit length – the volume opacity – is given by χ = κρ, where κ
is the mass opacity – the mass absorption coefficient. This linear-density absorption is
considered to be unaffected by clumping.
However, for individual clumps which are optically thick, the effective opacity can be
written in terms of the ratio of the physical cross-section of the clumps to their mass:
κeff ≡ l2
mc=
κ
τc; τc > 1 (1.13)
showing that, relative to atomic opacity, κ, the effective opacity is reduced by a factor
that scales with the inverse of the clump optical thickness, τc = κρcl = κ < ρ > l/f
The clump optical thickness that determines the effective opacity depends upon the
ratio of the clump scale to the volume filling factor – the ratio is called the porosity length,
h ≡ l/f .
The difference therefore between porosity and the aforementioned density-squared
clumping correction, which depends solely upon the filling factor, is that the porosity
also depends upon the scale length of the individual clumps.
The effective absorption of clumps is generally set by the geometric cross section mul-
tiplied by a correction for the net absorption fraction, σeff = l2[1 − exp−τc ] and applying
this to the scaling equation above, provides a general porosity reduction in opacity in the
form:
κeff
κ=
1 − e−τc
c
τc(1.14)
In the optically thick clump limit, τc ≫ 1, this leads to a reduced opacity of κeff/κ ≃1/τc; while in optically thin material, τc ≪ 1, it recovers the same opacity, κeff ≃ κ.
1.7. Investigations into Variability in Stellar Winds from OB Stars 51
1.7 Investigations into Variability in Stellar Winds from OB
Stars
Although knowledge existed of the variable nature of OB stars, a more detailed exploration
of this potentially interesting aspect of hot massive stars was brought about with the
advent of the International Ultraviolet Explorer (IUE) satellite. From the extensive UV
data available it soon became clear that hot star wind variability was ubiquitous and
therefore not so much a phenomenon isolated to perhaps a handful of such stars, but in
fact an intrinsic property of all hot stars. Because of this ever-fluctuating facet of the
stellar wind ‘behaviour’, single exposure UV spectroscopy can only provide perhaps a
glimpse of merely an average moment; but how would it be possible to tell – knowing that
the wind’s physical characteristics are ever-changing – that what one observes within the
UV spectra is a manifestation of a maximum or minimum flux, or some level in between.
As soon as evidence of varying wind signatures came to light, then the logical step was to
establish time-series studies, and from such multi-exposure spectra one could explore the
variable UV P Cygni profiles via more mathematical analyses of their flip-book nature.
The most immediate implication of the variable nature of the outflow was that all
measures of stellar mass-loss had to be revised as they were calculated based upon the
erroneous assumption of the steady-state of a given star’s continual loss of mass. In
order to more accurately predict stellar evolutionary stages and the timescales therein,
it is absolutely crucial to possess an accurate understanding of the mass-loss driving this
evolution (Massa et al. 1995).
From time-series UV spectra now available from IUE, new aspects of observation could
be exploited and subsequent theories derived. Through two-dimensional greyscale repre-
sentations of temporally-stacked one-dimensional spectra, it became apparent that certain
recurrent features could be observed (Prinja 1988; Prinja et al. 1992). The blueward mi-
gration of Discrete Absorption Components (DACs) – small but significant additional
absorption features found within the absorption troughs of P Cygni profiles – was seen to
be recurrent, and estimates of the modulation of this were found to be strongly correlated
with the proposed rotation velocity, v sin i, of the star.
The physical origins of these additional optical depth components started another
branch of speculation: as the temporal greyscale images showed that the DACs are initially
broad, then as they migrate through the absorption trough in which they appear, they
1.8. From O Stars...to Central Stars: Research Objectives 52
narrow while accelerating to higher velocities, it was speculated that the causes of these
additional structures was some form of disturbance upon the stellar surface.
Whatever the initial cause of the DACs, the mechanisms by which they travel out-
ward from the stellar surface and through the wind has been attributed to Co-rotating
Interaction Regions (CIRs) (Owocki 1994; Cranmer & Owocki 1996). Perturbations in
the radiative driving force at the stellar surface, causing alternating bright and dark spots
of localised increases and decreases in the radiative driving force, are carried outward,
co-rotating through the wind, as alternative regions of slow travelling, high density ma-
terial, and regions of faster, lower density. When the faster material catches up with the
slower material ahead, the two regions interact, and this is considered the direct cause
of plateau-ing in the velocity gradient of the accelerating wind: a key component in the
creation and subsequent appearance of the blueward-migrating DACs.
Therefore establishing the direct cause of the photospheric perturbations has proven
to be yet another challenge. One suggestion has been that the disturbances are caused by
structures in the magnetic field, but magnetic field measurements carried out by de Jong
et al. (2001) only produced a null-detection. An alternative potential source of the surface
disturbances are so-called Non-Radial Pulsations (NRPs), which have been developed as a
source following on from variability studies of photospheric absorption and emission lines
which have been shown to possess modulation periods: Reid & Howarth (1996) discovered
a modulation period of 19.6 hrs in the absorption profile of the photospheric Hα line of
the O supergiant ζ Puppis – a modulation akin to those discovered in the time-series UV
resonance lines spectra of B Supergiant HD 64760.
1.8 From O Stars...to Central Stars: Research Objectives
The main focus of this thesis is to extend the time-series-based analysis, hitherto performed
in the study of O and B star stellar winds, to those emanating from the Central Stars
of Planetary Nebulae. The investigations into this are will be set out and described as
follows:
In Chapter 2, descriptions are given of mathematical techniques behind time variance
and optical depth modelling of absorption line profiles.
The initial investigation is detailed in Chapter 3: an in-depth study of the stellar
outflow from the central star of the Cat’s Eye Nebula, NGC 6543, undertaken using time-
1.8. From O Stars...to Central Stars: Research Objectives 53
series FUV data taken from the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite.
The variable nature of the wind is uncovered as expressed via the temporal behaviour
of UV resonance absorption features, containing what appear to be Discrete Absorption
Components (DACs) akin to those discovered in the stellar winds of OB stars. Key features
are modelled also, providing further insights into their nature.
In Chapter 4, the search for wind variability is extended to other CSPNs, using (as far
as possible) similar analysis techniques where, although the ability to do this is somewhat
restricted because of the limited data available, further evidence of a structured nature to
CSPN outflows is presented.
And then in Chapter 5, the investigation into temporal variability is carried to the
very base of the wind where, using optical time-series data obtained via the ESO 3.6 m
telescope and the High-Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph,
the potentially-variable behaviour of photospheric absorption lines is tested in order to
provide clues to possible causes of the variability found further out in the stellar wind.
Finally in Chapter 6, the conclusions of the thesis are set out, and future investigations
proposed.
Chapter 2
Mathematical techniques
In this chapter a brief description will be given of the mathematical techniques used to
analyse time-series data in order to uncover the temporal behaviour and underlying physics
of stellar winds.
2.1 Equivalent Width (EW) Measurements
As a primary demonstration of the extent of the variability of the spectral absorption lines,
for each time-series exposure, the equivalent width (EW) of a given line will be measured:
the mean EW can thus be derived and more importantly the maximum and minimum EW
for each time-series can be noted and hence the maximum percentage variation from the
mean can be calculated.
Fig. 2.1. Diagram comparing the strength of a typical spectra absorption line,a, with its ‘equivalent width’, b.
54
2.2. Spectral Time Variance Analysis 55
As a measure of the strength of an absorption line profile, the equivalent width of
a given line is essentially a rectangular area between a normalised continuum and zero;
the width (W ) of the rectangle is such that the rectangular area is equivalent to the
integral area of the line profile beneath the level of the continuum, as shown in Figure 2.1.
Mathematically, the equivalent width, EW , is given by:
EW =
∫ λ2
λ1
Fc − Fλ
Fcdλ (2.1)
where Fc is the intensity of the normalised continuum, Fλ is the intensity profile of the
absorption line, and dλ is the integral sampling in wavelength space; the strength of
the profile is defined as the integral of the profile between λ1 and λ2, two points at the
extreme ends of the wings of the broadened absorption line where they merge back into
the continuum.
2.2 Spectral Time Variance Analysis
Each fits file-based spectra will be processed in four stages, each stage revealing a different
aspect of any variability which might be occurring: each of the following processes is
performed via an Interactive Data Language (IDL) package.
2.2.1 Temporal Variance Spectra (TVS)
As the aim of this project is to seek variability in the stellar outflows of central stars from
the observation and analysis of central star spectra, an initial aim must be to qualitatively
test these spectra for evidence of variability. This is achieved by passing a set of time-
series spectra through a temporal variance programme. This measures the inherent flux
variability of each bin in either wavelength or velocity space for each spectra in the selected
series and produces a temporal variance spectrum for the given wavelength/velocity range
for the series.
The IDL commands executed during this procedure are as follows:
• load fits ts: The time series to be analysed is loaded.
• define continuum: With this command, coupled with the given name of the input
dataset, a simple integer-based command structure appears whereby the normalised con-
2.2. Spectral Time Variance Analysis 56
tinuum of the time-averaged spectrum – appearing in a separate window – can be defined
in space by short wavelength sections about the targeted line profile.
• dug tvs: Using the continuum sections as defined in the previous step, the TVS
algorithm then statistically analyses the continuum, including the behaviour of the noise
levels therein, to assess the basic level of variation. From this initial analysis the TVS
predicts a 95% confidence level (roughly 2 standard deviations from the mean variability
of the continuum) which it uses as a guide by which any variabilty along the line profile
which is greater than this indicates a significant level of activity in the line profile and
which requires further investigation.
To calculate the TVS for a given spectra series the following equation is applied:
TV Sj =1
N − 1
N∑
i=1
d2ij (2.2)
(Fullerton et al. 1996)
Here the j th wavelength pixel of the ith spectrum of N spectra in a given dataset. dij
is called the residual spectrum and is defined by:
dij = Sij − sj (2.3)
where Sij represents a specific matrix element and sj is the column average given by:
sj =1
N
N∑
i=1
Sij (2.4)
The TVS spectrum produced is a plot of the calculated TVS against either wavelength
or velocity of the line profile. Any variability within the spectra is recorded and displayed
upon the TVS spectrum: an example of TVS applied to the Pv λλ 1117.98, 1128.01 dou-
blet is shown in Figure 2.2.
In practice, the output images display the wavelength-dependent variations of (TV S)1
2 ,
instead of TV S: this is because the rooted TVS scales with the spectral deviations, giving
a more accurate impression of the relative amplitudes of line profile variations from star
to star (Fullerton et al. 1996).
2.2. Spectral Time Variance Analysis 57
6.0
8.0
10.0
12.0
14.0
16.0
18.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.4
0.6
0.8
1.0
1.2
1.4
Flu
x
Fig. 2.2. Time Variance Spectra (TVS) of the most developed P Cygni absorp-tion doublets from the F034 time-series spectra of PN NGC 6543: the well-developed but unsaturated Pv λλ 1117.98, 1128.01 doublet is clearly stronglyvariable across both the blue and red absorption troughs of the doublet, showingbroad peaks above the dotted 95% confidence line
2.2.2 Greyscale I
Using the information obtained in the TVS stage i.e. where along a given spectra no-
ticeable variance is occurring and particularly at which spectral lines variability is most
pronounced, one is able to produced a visually descriptive means by which one can display
flux variability of spectral lines along the timescale given for a particular observing run.
The IDL commands are as follows:
• load fits ts: The time series is loaded as above.
• greyscale: The time series is fed into the greyscale algorithm and a GUI window is
displayed in which are displayed various parameters of the input data, the values of which
can be altered for preferential displays. For instance the first two boxes, xlow and xhigh
contain the values of the wavelength extremities of the loaded time series; a third box,
Rest Wavl – rest wavelength, is, by default, set to zero. With these default settings the
spectrum displayed beneath the corresponding greyscale is simply labelled by wavelength;
however, if a value is entered for the rest wavelength e.g. for the rest wavelength value
2.2. Spectral Time Variance Analysis 58
of a particular absorption or emission line, then the algorithm will convert the spectrum
readout from wavelength space to velocity space, and hence the rest wavelength will be
converted to the zero-value of velocity. In this case the values entered into the xlow and
xhigh boxes must be in terms of velocity, and therefore represent the extent of blueshift
(the xlow box) and redshift (the xhigh box) which is required for the spectrum displayed
in the greyscale output – the velocity space Doppler shift can therefore set to as close to
or as far from the zero shift velocity (taken from the given rest wavelength).
Another of the GUI input settings which yields a significant output is the option to
subtract, or alternatively divide by, the mean flux levels from the varying intensity
values produced by the algorithm and so the resultant greyscale is now a more accurate
depiction of the variable nature of the time series flux with the extreme of black and
white representing levels of ± 2 standard deviations in from the mean flux, therefore any
excessive flux from the average is represented by the lighter grey to white end of the scale;
any flux reduced below the average is thus represented by the darker grey to black end.
• greyscaleplot: The greyscale calculated by the algorithm is displayed with a mean
spectrum of the time series across the bottom as a reference to the greyscale plotted
directly above. Using this plot it is possible to see whether any evidence for variability
exists.
The greyscale of these dynamic spectra is, in its relation to the average flux, a “differ-
ence flux”.
2.2.3 Two-dimensional Fourier analysis: power spectra
The discovery of variability with the outflow is only the first step. What is required is to
uncover a form of periodic variability, and to do this the technique of Fourier analysis is
utilised.
Fourier analysis uses the theory that any periodic function f(x) can be broken down
to (and subsequently re-synthesised as) a series of sinusoidal functions:
f(x) = a0 +∞∑
k=1
(akcoskx + bksinkx) (2.5)
where the coefficients a0, ak and bk are given by:
2.2. Spectral Time Variance Analysis 59
a0 =1
2π
∫ 2π
0f(x)dx, ak =
1
π
∫ 2π
0f(x)cos(kx)dx, bk =
1
π
∫ 2π
0f(x)sin(kx)dx (2.6)
Therefore in applying Fourier techniques to a given set of time series spectra one can
attempt to discover whether any such periodic variability exists or not. In order to un-
cover time-based periodic functions the spectra are passed through a Fourier transform
algorithm. Time-dependent functions can be represented by a superposition of +/− com-
ponents throughout the entire frequency range:
f(t) =
∫ +∞
−∞
dνF (ν)e+2πiνt,−∞ ≤ t ≤ +∞ (2.7)
(Roberts et al. 1987).
The function f is therefore given by the superposition of the Fourier transform and
the contribution of each ν to f is thus defined.
The Fourier transform itself is given by:
F (ν) ≡ FT [f ] ≡∫ +∞
−∞
dtf(t)e−2πiνt (2.8)
for −∞ ≤ ν ≤ +∞.
The plotted Fourier transforms – the power spectra – depict the contribution of ν to
the variance of f thus:
P (ν) = |F (ν)|2 (2.9)
for −∞ ≤ ν ≤ +∞.
It should be pointed out, however, that Fourier transforms only work in an effective
manner when the function under analysis is continuous; whereas the spectral sections
being fed into the Fourier transform algorithm are, by their very nature of being of a
restricted wavelength range, finite. This causes problems with the outputted frequency
power spectrum: noise is created by the transform trying to cope with a finite function,
2.2. Spectral Time Variance Analysis 60
resulting in numerous ghost frequencies being displayed within the output spectrum.
To solve this the output power spectrum is then passed through a cleaning algorithm
which works by identifying the strongest peaks in the power spectrum and then removing
a fraction – the ‘gain’ – of them. This process is repeated over and over until what remains
in the output is the noise only i.e. what has been removed is the required noise-less power
spectrum.
Again, the requisite IDL commands are as follows:
• load fits ts: The time series data files are loaded as before.
• fourier2d: As with the greyscaling process, the input time series is fed into the
algorithm but before set in motion a GUI window appears in which various processing
and display parameters can be adjusted. Among these are two which affect the way in
which various possible frequencies are tested against the inputted time series in the Fourier
analysis: df adjusts the spacing between consecutive test frequencies, and fmax sets the
upper limit of the test frequencies, in cycles per day.
For the purposes of the initial experiments with this system, each of the line profiles
was tested with upper limits of test frequency of 12, 14, 16, 18 and 20 cycles per day, each
with a frequency spacing of 0.2 cycles per day.
As with the greyscale GUI there are also boxes contained within the fourier2d GUI
where the rest wavelength of the given line profile, and the limits for both the blue and
redshifted velocities either side of the zero velocity of the rest wavelength, are entered.
• fourier2dplot: The two-dimensional Fourier transform power spectra is displayed
with a mean spectrum about the selected line plotted at the bottom of the display and
above which appears the result of the two-dimensional Fourier analysis. The pattern of
dots displayed is interpreted at the top and to the right hand side: effectively the dots
and broader markings are added up in two different directions:
• 1: Added vertically (and working form left to right) the markings reveal the variance
along the line profile and indeed the graph at the top of the display is similar to that of
the TVS plot for the similar line profile.
• 2: Added horizontally (and working from bottom to top) the markings reveal the
strength of response to each test frequency – the power of each test frequency (labelled
from up the left hand side from zero to the fmax value) over the extent of the test range:
figure 3.
It is the right hand side power spectrum which shows the frequencies most likely to
2.2. Spectral Time Variance Analysis 61
be occurring with the variability of the time series spectra. Often a large peak occurs at
the top near the fmax value but this is simply a normal product of the algorithm. The
main frequencies contained within the time series should be revealed by the larger peaks
between zero and the maximum, however as mentioned above, unless the cleaning process
has been undertaken there may be many false peaks appearing within the power spectrum
due to noise caused by the discontinuous nature of the line profile. Once cleaned, a more
reliable power spectrum should reveal the period(s) inherent in the time series. Examples
of Fourier analyses output are shown in Figure 2.3.
−1000 −900 −800 −700Velocity (km/s)
0.4
0.5
0.6
0.7
0.8
Flu
x
0 2 4 6 8Power x 10−4
0
5
10
15
201.1
1.8
2.5
3.2
Pow
er x
10−
4
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
−1000 −900 −800 −700Velocity (km/s)
0.4
0.5
0.6
0.7
0.8
Flu
x
0.5 1.0 1.5 2.0Power x 10−4
0
5
10
15
200.8
2.3
3.7
5.2
Pow
er x
10−
5
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
Fig. 2.3. Full-panel displays of Fourier-based frequency analysis of the bluetrough of the P v doublet, as seen in the F034 spectra of PN NGC 6543, analysedbetween −600 – −1100 km s−1, with the ‘dirty’ analysis on the left, and the ‘clean’analysis (gain = 0.500) on the right.
2.2.4 Greyscale II
Once potential periods of cycle have been identified from the cleaned power spectrum
then the greyscale technique can be reapplied and now, using the GUI window appears it
contains a box in which one is able to enter the test period (i.e. the frequency as displayed
by the Fourier power spectrum but inverted) and can also indicate that the output is
2.3. Analysing Line Profiles within the Wind: SEI Code 62
‘folded’ so as to display this periodic variability. The folding technique essentially takes
the period value as entered in the greyscale GUI and then compares the input time series
data comparing its time axis with the different phases of the period as applied. It then fills
in any phase gaps across the timescale of the data with greyscale sections of comparable
phase from elsewhere along the same timescale. When all gaps have been filled – the data
effectively folded in on itself – then the output displays another greyscaled image but with
the vertical axis scaled to one (or more) period(s): see Figure 2.4.
Fig. 2.4. Greyscale representation of the F034 P v doublet of PN NGC 6543,folded over a period of 0.172 days – here displayed over three cycles.
2.3 Analysing Line Profiles within the Wind: SEI Code
The study of line profiles in stellar spectra can reveal fundamental information about the
wind: they can reveal physical details about the structure of the wind, as well as more
2.3. Analysing Line Profiles within the Wind: SEI Code 63
intrinsic qualities by conveying information about mass-loss. Spectral line profiles can be
in emission, absorption or in combination, such as within the P Cygni profiles found in
UV spectra of OB stars; or as investigated in this thesis, the FUV spectra of CSPNs. The
way to extract this information is to computer model of the given wind profile on top
of that observed in the spectra, and from a comparison of the two, one is able to obtain
information of the velocity law governing the wind, and also to derive the column density
and understand the distribution of the ions under observation, as a function of velocity.
To this end, the Sobolev with Exact Integration (SEI) method is employed for the
purpose of generating model fits to the P Cygni profiles found in both the UV (IUE) and
far-UV (FUSE) wave-bands. The model P Cygni fits yield measurements of wind optical
depths as a function of velocity for each ion analysed; the results are given as a product
of the mass-loss rate and the ionisation fraction, Mqi(v)
The method works by first evaluating the source function using the Sobolev approxi-
mation, where for a fast accelerating stellar wind the source function is calculated using
the escape probability method. The approximation treats the line absorption coefficient as
a delta function in frequency: this is allowed if the velocity gradient, dv/dr is much larger
than the vt/l fraction, where vt represents the combined thermal and turbulent velocity
for ions in the wind, and l is the characteristic length over which either the density or ion-
isation changes Lamers et al. (1987). Then the radiative transfer equation can be solved
accurately, and thence calculating line profiles occurring within the expanding stellar at-
mosphere via a monotonically accelerating velocity law in which random chaotic motions
can be treated as a one-dimensional radial turbulence (and for which a radially dependent
macro-turbulent parameter was introduced to the method by Haser et al. (1998)), thereby
modelling small-scale perturbations in the velocity law.
The Source Function
The source function of a two-level atom is given as:
Sν(x) = [βc(x)I∗ν + ǫ′Bν(x)]/(β + ǫ′) (2.10)
where I∗ν is the stellar intensity at frequency ν of the radiation leaving the photosphere, βν
is the Planck function of the wind, and ǫ = Cul/Aul is the ratio of collisional to radiative
2.3. Analysing Line Profiles within the Wind: SEI Code 64
de-excitations. Here β is the escape probability for line photons:
β(τ0, σ) =
∫ 1
0
(
1 + σµ2
τ0
)[
1 − exp
(
− τ0
1 + σµ2
)]
dµ (2.11)
and βc is the penetration probability for continuum photons:
βc(τ0, σ, z) =1
2
∫ 1
µc
(
1 + σµ2
τ0
)[
1 − exp
(
− τ0
1 + σµ2
)]
dµ (2.12)
where
σ =x
w
dw
dx− 1 (2.13)
and µc = (1 − z2)1/2
The optical depth above is defined as:
τ0(x) =πe2
mc(gf)lu
(
nl
gl− nu
gu
)
R⋆
v∞
c
ν0
x
w(2.14)
However, for resonance lines nu/gu ≫ nl/gl and so the optical depth can be approxi-
mated by:
τ0(x) ≈ πe2
mcfλ0ni
x
w
R⋆
v∞(2.15)
where ni is the number of ions per unit volume.
In a case where the photospheric spectrum contains a continuum Ic with an absorption
line, then
I⋆ν = Ic[1 − A(ν − ν0)] (2.16)
where A is the absorption.
2.3. Analysing Line Profiles within the Wind: SEI Code 65
The intensity at a distance x, frequency ν0, and angle µ is given by:
Iν0(x, µ) = Ic[1 − A(∆ν ′)] (2.17)
where ∆ν ′ = ν0v∞w(x)µ/c. The penetration probability βc of the contribution of the
continuum photons to the mean intensity Jν becomes:
βc(τ0, σ, z) =1
2
∫ 1
µc
[1 − A(∆ν ′)] ×(
1 + σµ2
τ0
)[
1 − exp
(
− τ0
1 + σµ2
)]
dµ (2.18)
where β remains as before.
Solving the Transfer Equation
The solution to the transfer equation gives the intensity as seen by the observer for a line
of sight p as:
Iν(p) =
∫ z=∞
z=−∞
Sν(z′)e−τν(z′)dτν(z′), (2.19)
for p ≥ 1
Iν(p) =
∫
−z⋆
z=−∞
Sν(z′)e−τν(z′)dτν(z′) + I⋆νe−τν(−z∗), (2.20)
for p < 1
The second part of the equation describes the intensity coming from the line of sight
intersecting the star at z = −z∗ = −(1 − p2)1/2 and containing a contribution from the
photospheric radiation I∗ν .
The optical depth in the expression for Iν(p) is:
τν(z′) =
∫ z′
∞
τ0(x)Φν(z)/(1 + σµ2)dz (2.21)
where the integration is made along a line of sight of constant p.
2.3. Analysing Line Profiles within the Wind: SEI Code 66
In this expression the profile function Φnu(z) is determined by the local turbulence in
the wind. If φ is expressed in terms of the dimensionless velocity w:
φ(∆ω) = π−1/2w−1D exp[−(∆w/wD)2] (2.22)
with w2D = w2
T + w2t , where wT = vturb/v∞ and wt = vthermal/v∞, then Φν(z) is defined
by:
Φν(z) = φ
[
∆w = µw(x) − ν − ν0
ν0
c
v∞
]
dwz
dz(2.23)
where z and x are coupled by the condition that p is constant.
The flux, normalised to the continuum, is given by:
Fν =
∫
∞
0[Iν(p)/Ic]2pdp (2.24)
The parametrised velocity law is given as:
w(x) = w0 + (1 − w0)(1 − 1/x)β (2.25)
often with β = 1 and w0 = 0.01. The parametrised optical depth is given as:
τ1(w) = T (γ + 1)(1 − w0)−1−γ(1 − w)γ (2.26)
where τ1(x) is defined:
τ1(x) =πe2
mcfλ0ni
dr
dv= τ0(x)
d ln x
d ln w(2.27)
However, with a modified code (see Massa et al. 2003), the optical depth is set by
adjusting that as set by 21 velocity bins, each approximately 0.05v∞ wide.
2.3. Analysing Line Profiles within the Wind: SEI Code 67
The following section describes in detail the component parts of the SEI code calcula-
tions.
2.3.1 The SEI Method
The SEI method assumes a homogeneous, spherically symmetrical wind, progressing with
smoothly accelerating velocity laws. It can be used to model either single absorption lines
but has the ability to accommodate the blending of closely-spaced doublets also.
The various input parameters are as follows:
1. Terminal velocity: a measure of v∞ is required in order to calculate the normalised
velocity parameter, w ≡ v(r)/v∞.
2. Velocity law: a standard parametrised β-law is assumed to represent the expansion
and acceleration of the wind. This has the form:
w = w0 + (1 − w0)
(
1 − 1
x
)β
(2.28)
where x = r/R∗ and R∗ is the stellar radius (Lamers et al. 1987). w0 is set as 0.01 in all
calculations. The value of β determines the shape of the overall profile – it governs the
density distribution, ρ(x), as described via the equation of mass continuity:
The shape of the entire distribution of the wind is set by the value of β: it controls
the density distribution as given my the Mass Continuity equation:
M = 4πR⋆2v∞x2w(x)ρ(x) (2.29)
3. Turbulent velocity: is depicted by a Gaussian distribution, with a 1 σ dispersion
parameter wD. It is an additional effect added to account for an include such effects as
shocks in the wind upon the line profile. It smooths the distribution of optical depth as a
function of w – its extends saturated portions of strong P Cygni profiles by ‘a few times
w’ – it notably decreases the sharpness of the absorption trough near v∞, and spreads out
the profile in that it shifts the maximum velocity in absorption blueward and the strength
of the emission peak redward.
4. Photospheric spectrum: this is given by a Gaussian distribution of optical depth.
2.3. Analysing Line Profiles within the Wind: SEI Code 68
rw = exp
{
−τB0 exp
(−w2
σ2w
)
− τR0 exp
[−(w − δw)2
σ2w
]
}
(2.30)
where τR0 /τB
0 = fR/fB the ratio of the oscillator strengths for the doublet (or zero for a
singlet); δw is the spacing of the doublet in normalised velocity; and σw is related to the
full width of the line expressed as a velocity, vG, by vG = 2(ln2)1/2σwv∞.
5. Optical depth of the wind: this is given from the radial Sobolev optical depth,
τrad(w), which is derived/modelled from 21 independent velocity bins which are individu-
ally adjusted to provide the best model fit for the spectrum of the wind line – the optical
depth is the only remaining free parameter to be tested once the terminal velocity and the
photospheric spectrum are fixed.
In fitting the model wind profile in this manner, the adjustment of the standardised-
velocity-dependent optical depths is reliant upon the premise that in a monotonically
expanding spherically symmetric outflow, only material with w ≤ w + wD contributes to
the formation of the line, (as given in Lamers & Cassinelli 1999).
The fitting itself is achieved by first adjusting the level of the optical depth velocity bin
at w = 1 i.e. at the blue-ward terminal velocity edge of the P Cygni profile of the given
stellar wind absorption line under scrutiny. Thence fits are obtained for each velocity bin,
in steps inward of the wind, with adjustments made for optical depth for each wi until a
satisfactory fit of the profile is made at each of the 21 points.
If all assumptions concerning spherical symmetry and the monotonic simplicity of the
β-law are correct, then the fits to τrad(wi) can be regarded as reliable.
6. In manipulating the optical depth levels for each of the 21 velocity bins, what in fact
is actually being derived is the ionisation level for each of the bins along the velocity profile.
This is because the ionisation profile of each bin, qi(w), is related to the corresponding
optical depth optical depth, τradi(w) (see Olson 1982) by
qi(w) =mec
πe2
4πµmH
fλ0AE
R⋆v2∞
Mx2w
dw
dxτrad(w), (2.31)
where qi(w) is the fraction of element E in ionisation state qi at (standardised) velocity
w. M is the mass-loss rate of the star, v∞ is the wind’s terminal velocity i.e. the factor by
2.4. A Brief Introduction & Description of TLUSTY 69
which the profile’s velocity bins are standardised, µ is the mean molecular weight of the
plasma – set to 1.35 for all stars, AE is the abundance of element E relative to Hydrogen.
The Key Steps of the Fitting Procedure
• Estimation of interstellar H1 and H2 column densities – solar abundances assumed for
all objects in this thesis.
• A saturated wind line is used to provide parameter values for the wind law, namely
the acceleration profile factor β, the terminal velocity of the wind v∞, and wD, the wind
turbulent velocity factor. The line used is usually the C iv λλ 1548,1550 doublet - this is
strongly saturated and therefore sensitive to the wind’s terminal velocity – the farthest
blueward edge of the 1548 A line is where the blue-shifted terminal velocity is measured.
• An estimate of the size and shape of the input photospheric spectral line being modelled
is obtained using the spectral line rotational broadening program TLUSTY (see below).
• As stated above, once the velocity law parameters of β, v∞, and wD have been set,
resonance lines are finally fitted through the adjustment of 21 velocity bins in the form of
a histogram of τrad.
2.4 A Brief Introduction & Description of TLUSTY
Following advances in observational data and computational abilities Lanz & Hubeny
(2003) were encouraged to adopt the physically sound and powerful Accelerated Lambda
Iteration (ALI) which, combined with a wealth of atomic data available via such projects
as the Opacity Project (Seaton 1987), the IRON project (Hummer et al. 1993), and the
OPAL project (Iglesias & Rogers 1991), provided the raw materials from which to derive
physically accurate stellar atmosphere models.
Various driving factors which warranted the application of advanced techniques to
produce such stellar atmosphere models included the ongoing investigations into stellar
outflows of O-type stars, necessitating theoretical departures from local thermodynamic
equilibrium (LTE) assumptions while at the same time combining the effects of atmo-
spheric line blanketing, particularly via the thousands of iron group lines found in such
outflowing atmospheres.
Also, the development of so-called ‘unified’ stellar model atmosphere codes – such as
CMFGEN (introduced in the next chapter) – which aim to construct models from the
2.4. A Brief Introduction & Description of TLUSTY 70
stellar surface right out into the wind, also require, for the desire of accuracy, to be able to
include metal line blanketing in such an nLTE atmosphere. However, whereas CMFGEN
employs spherical symmetry in its construction of a ‘unified’ atmosphere, thereby extend-
ing the model into the wind; TLUSTY assumes the simpler plane-parallel geometry to
develop an accurate description of the stellar photosphere, thereby providing an accurate
lower boundary for stellar wind models.
The Complete Linearisation (CL) method, introduced by Auer & Mihalas (1969) pro-
vided a computational platform from which it was possible to simultaneously solve the
equations of radiative transfer, hydrostatic equilibrium, radiative equilibrium, and also
those of statistical equilibrium: physically it was the appreciation of the effect of coupling
parameters such as energy level populations with the radiation field and its temperature,
that provided the initial conceptual breakthrough; unfortunately at the time the limita-
tions of computer power meant that only a very few energy levels of only a handful of
lines could be dealt with, out of the potential millions.
It then became apparent that the monumental task of mathematically solving radia-
tive transfer, etc., for all these lines, could in fact be simplified through by a combina-
tion of mathematical breakthroughs: firstly, the introduction of Anderson’s superlevels
(1985,1989) – collating all individual frequencies into select frequency blocks, whereupon
radiative transfer is solved explicitly for a given block, and solutions for individual con-
stituents of the block are converged iteratively.
The application of powerful iteration techniques provided another breakthrough, par-
ticularly the development of ordinary lambda iteration into the accelerated version. Here,
the introduction of the approximate lambda operator acts upon the source function, plus
a correction term from the previous iteration, rapidly, and accurately, reduces the com-
putation time for complex line-blanketed atmospheres. A description of the accelerated
lambda iteration technique is given below, followed by a brief introduction to Anderson’s
superlevels.
2.4.1 Accelerated Lambda Iteration (ALI)
Accelerated Lambda Iteration (ALI) is the key powerful computational technique employed
in the TLUSTY method in its production of a modelled stellar atmosphere. In simple
terms – for example for a 1-D homogenous static medium – the main task is to solve
the both the radiative transfer equation (which is both angle and frequenct dependent)
2.4. A Brief Introduction & Description of TLUSTY 71
and the equation of statistical equilibrium: in combination, these equations can be solved
iteratively, but because of the angle-frequency coupling of radiative transfer which leads
to a matrix repersentation of the atmosphere, the iteration involved is unfortunately too
time consuming (Hubeny 2003).
Stellar atmosphere solving iteration begins with the angle-and-frequency-dependent
radiative transfer equation can be written:
µdIµν
dτµν= Iµν − Sν (2.32)
where µ = cos θ
The formal solution to this may be written:
Iµν = Λµν [S] (2.33)
where Λ operates on the source function. Through integration the frequency-averaged
intensity can be given as:
J = Λ[S] (2.34)
where:
J =
∫
Jnuφνdν (2.35)
and:
Λ =
∫
Λνφνdν (2.36)
with φν is the normalised absorption profile.
2.4. A Brief Introduction & Description of TLUSTY 72
Jd =
D∑
d′
Λdd′Sd′ (2.37)
The equation of statistical equilibrium which in a simple two-level atom can be written:
S = (1 − ǫ)J + ǫB (2.38)
where ǫ is the collisional probability and B is the Planck function.
In substituting Equation 2.34 into Equation 2.38, the source function can be written:
S = (1 − ǫ)Λ[S] + ǫB (2.39)
and if Λ were linear, then the solution can be arrived at in one step:
S = [1 − (1 − ǫ)Λ]−1ǫB (2.40)
Unfortunately Λ is in reality a matrix and its implied inversion is by no means a simple
matter and particularly time-consuming.
It can be solved however through iterating between the intensity and the source func-
tion, where successive solutions can be found thus:
Sn+1 = (1 − ǫ)Λ[Sn] + ǫB (2.41)
This is the essence of Lambda Iteration. Unfortunately, this method can be tremen-
dously time-consuming, taking a very long time before convergence is achieved; there is
also a tendency for the solution to stabilise, with differences in successive solutions becom-
ing negligible thereby reaching a conclusion before the correct solution has been obtained.
A much faster iteration method can be afforded by so-called operator splitting, where
the Λ operator is written as:
2.4. A Brief Introduction & Description of TLUSTY 73
Λ = Λ∗ + (Λ − Λ∗) (2.42)
where Λ∗ is an approximate lambda operator. Now the iterative-solving equation can be
written:
Sn+1 = (1 − ǫ)Λ∗[Sn+1] + (1 − ǫ)(Λ − Λ∗)[Sn] + ǫB (2.43)
The exact operator is now split into two contributions: the approximate Λ∗ operator
acts upon the new iterate of the source function, and the difference between the exact and
approximate operators acts upon the the previousm known source function.
The source function is now iterated to convergence – despite using an approximate
operator – and so radiative transfer is solved exactly.
An alternative from of the above equation can be formed using a so-called immediate
source function taken from the old source function by the formal solution (FS):
SFS = (1 − ǫ)Λ[Sn] + ǫB (2.44)
and so the diffrence bewteen successive iterations can be expressed thus:
δS ≡ Sn+1 − Sn = [1 − (1 − ǫ)Λ∗]−1 [SFS − Sn]
(2.45)
2.4.2 Simplification through Super-levels
When attempting to deal with iron species line blanketing one soon discovers that any
iteration code has to somehow deal with 104 – 105 energy levels and consequently 106 – 107
energy transitions: such incredible complex calculations would tax even the most rapid
computational machinery, and so clearly some method need to be found to somehow reduce
the complexity of these calculations without unduly robbing the user of all important data
which might otherwise be lost through over-simplification (Hubeny & Lanz 1995).
In order to be able to deal with the thousands upon thousands of lines encountered in a
2.4. A Brief Introduction & Description of TLUSTY 74
line blanketed stellar atmosphere, Anderson (1989) introduced the concept of ‘superlevels’:
here a great many energy levels can be grouped together so that a large number of energy
levels, j, can be formed into a superlevel, J , their common factor being that they possess
the same nLTE departure coefficient – that is to say they all the j components are in
Boltzmann equilibrium with respect to one another.
Anderson (1989) and later Dreizler & Werner (1993) partitioned the true levels into
superlevels based upon their energies only, and so the number of superlevels was small, 7
to 8 per degree of ionisation. However Hubeny & Lanz (1995) considered this too much of
a simplification because the subsequent wide energy widths of the superlevels would not
reflect the true nature of indvidual transitions, and also transitions between components
of an given superlevel have to be considered.
In choosing the number and nature of the superlevels, one must decide how to sort out
the innumerable levels into these. Clearly the individual energies of the level components
must be close and possess similar properties i.e. they should belong to the same spectro-
scopic multiplet, have the same parity, etc.; but there should not be too many superlevels
chosen as this would defeat the object of this attempt at simplification.
So accordingly, all levels within a superlevel must possess similar parity, and differences
between energy levels must be small. This has the result that there are 10 – 15 superlevels
per system and so 20 – 30 superlevels per ion (Hubeny & Lanz 1995). In putting together
these superlevels only the those with measured energy levels, and not predicted ones, are
considered: high-energy levels are considered separately via appropriate partition functions
(see Hubeny 1988).
2.4.3 The Incorporation of the TLUSTY Models into the SEI Code
One of the main initial parameters to be fed into the SEI code – perhaps the most funda-
mental – is that of the photospheric profile of the resonance line under investigation, and
particularly is shape: its depth and width: the depth giving an indication of the level of
absorption/absorbers present and the particular frequency; the width giving an indication
of the scale of the stellar rotation which broadens the spectral line.
An estimate of the depth and FWHM width of the photospheric absorption line to
be used as an input for the SEI code can be provided by the TLUSTY grid of models
which essentially provide one with an estimate of the shapes of absorption lines as they
are affected by the rotation of a star of a given temperature and surface gravitational
2.4. A Brief Introduction & Description of TLUSTY 75
acceleration.
When downloaded, the TLUSTY grid of models presents the user with a range of
model stellar spectra of different values of surface temperature and (logarithmic) surface
gravity, each combination of Teff and log g having two files: one containing the spectral
line information, the other containing that of the model continuum. The spectra and
continuum corresponding to the Teff and log g of the star under investigation (or as close
to it as possible) are chosen.
For a given stellar wind UV resonance line or lines e.g. the P v λλ 1117.98,1128.01
doublet, an small section of the overall TLUSTY model spectral range – say approximately
100 Ai.e. ∼ 50 Aeither side of the singlet/doublet under investigation – is fed into a simple
rotationally-broadening algorithm, ROTIN, for which an approximate ‘typical’ rotational
velocity (v sin i) of 100 km s−1 is selected.
The resultant (broadened) spectra output can then be viewed through a standard
analysis tool such as DIPSO, and a measurement taken of the FWHM of the rotation-
ally broadened spectral line, which can then be used for the FWHM value for the input
photospheric absorption line for the SEI model. The TLUSTY output spectrum is also
normalised – as will be the input spectrum for the SEI code – and so a simple visual check
will give an estimate of the initial optical depth required by the photospheric absorption
line before it is affected by the motions of the stellar wind in the SEI model.
2.4.4 Example of an SEI Model Fit – Description of Panels
To illustrate a typical result of an absorption line fit using the SEI method, Figure 2.4 is
given as an example:
• Top panel:
This depicts the SEI-generated stellar wind model overlaid on top of the observed spec-
trum. The rest position of the red component of the doublet is indicated by a thick tick
mark along the normalised velocity axis. As well as the resultant model profile, the panel
also shows the component parts of the model, namely the direct (transmitted) and diffuse
(scattered) components, shown as respective dotted and dashed lines. These aspects of
the model fit can help to assess the validity of the parameters used to construct the model.
The addition of optical depth to decrease the transmitted flux at a high velocity will subse-
quently increase the forward-scattered component at low velocities within the absorption
trough of the P Cygni profile. Once the increase of high-velocity optical depth/absorption
2.4. A Brief Introduction & Description of TLUSTY 76
Fig. 2.5. SEI model fit of the mean spectrum from the F034 dataset of the UVspectra of the P v doublet, from the Central Star of PN NGC 6543; see text fordetailed descriptions of the individual panels.
produces more scattered light than the observed profile at lower velocities – thereby raising
the dashed scattered component line above the observed profile – then even with a further
addition of arbitrarily large optical depths at lower velocities will not be able to depress
the model line below the position of the scattered component. The only way to deepen
the low-velocity absorption in to either strengthen or widen the inputted photospheric line
profile, and if that does not improve the fit then the validity of the model’s assumption –
particularly the spherical symmetry – must be questioned.
• Bottom-left panel:
Here the histogram of optical depth, τrad, versus normalised velocity function, w = vi/v∞,
for the 21 independent velocity bins is shown; the optical depths displayed are those giving
the above SEI model its final best-fit form.
• Bottom-right panel:
Here can be seen the profile of the photospheric input absorption line which will be ul-
2.4. A Brief Introduction & Description of TLUSTY 77
timately modified with its progress through the stellar wind, taken from the TLUSTY
model grid for the star’s given effective temperature, Teff , and the logarithmic value of its
surface gravity, log g; its photospheric depth and width are estimated from the rotationally
broadened output of the particular ion absorption line as calculated via the ROTIN pro-
gramme. The normalised flux of the line is displayed versus the v∞-standardised velocity,
as with the adjacent velocity bin histogram.
Chapter 3
Seeking Structure in
UV Spectra of NGC 6543
3.1 Motivations
Investigating the mechanisms of mass-loss is crucial to the study of the development of
a stellar system, as the rate at which a star loses its mass is the key factor pertaining
to the development of a star, particularly during the latter stages of its life. The rather
commonplace existence of a stellar wind became evident from studies of UV data obtained
via the International Ultraviolet Explorer (IUE ) satellite, whence the streams of data dis-
played a wealth of P Cygni profiles from which the stellar wind velocities were measured;
and it was shown that the maximum speeds could be up to a few 1000 km s−1 and subse-
quent estimates of the mass-loss rate were shown to range between ∼ 10−11 and ∼ 10−6
M⊙ yr−1(e.g. Perinotto 1989).
From the the earlier evidence of the existence of a stellar wind, it has also been shown
that, more often than not, this wind can exhibit a number of varying characteristics:
these can found in radial velocity variations (Mendez et al. 1990); also variations have
been recorded in the shape-shifting spectra of a star, both in photometric variations of
the near-photospheric development stages of the wind as viewed in optical wavelengths
(Bell et al. 1994), or in the more fully accelerated outer regions as seen in the blueward
UV regions (Patriarchi & Perinotto 1997).
78
3.1. Motivations 79
One of the main reasons for seeking evidence for inhomogeneous wind structure is that
the stellar wind provides key estimates of the mass-loss rates of its parent star, and so a
non-spherically-smooth wind would indicate that current estimates for mass-loss rates are
inaccurate as they are based upon models which assume a spherically-smooth wind profile.
In fact the presence of inhomogeneity in the wind may indicate that previous mass-loss
rates have been over estimated by a factor of at least 3, and perhaps as high as 10 (see
Massa et al. 2003; Bouret et al. 2005; Fullerton et al. 2006b).
Past studies of fast wind variability spectra have utilised UV data collected by the IUE
satellite; but as well as being rather limited in number of exposures available, the UV res-
onance lines contained therein have been far too saturated to be able to provide sensitive
diagnostics – and changes between spectra have been hidden except for the extreme blue
edges of the line profiles. Also the IUE exposures were of the order of ∼ 2 – 3 hours which
is comparable to the wind flushing times in such stars. Therefore, in order to get a better
perspective on fast wind variability, we have sought to exploit the high-resolution capa-
bilities of the FUSE satellite which is capable of providing high signal-to-noise data over
relatively short integration times – as well as providing access to unsaturated resonance
line profiles – P v , S iv , S vi , and O vi .
3.1.1 The Target – NGC 6543
This chapter presents a time-series study of the HD 164963, the central star of the plan-
etary nebula NGC 6543, more commonly known as the ‘Cat’s Eye Nebula’. HST images
of the nebula reveal complex bipolar structures which include bubbles and precessing jets
(Wesson & Liu 2004).
The HST Wide Field Planetary Camera 2 (WFPC2) images taken via the Hubble Space
Telescope (HST ) (Harrington & Borkowski 1994) have provided the source material for a
quantitative analysis of the physical and ionisation structures found therein (Balick 2004).
The most immediately striking aspect of the HST images of the nebula is its complicated
knotted structure: The elliptically-shaped core is ∼ 12′′ along its major axis, and its minor
axis of the core has a slightly hourglass appearance. Within this region it is a further two
crossed ellipses that give the nebula its nickname of the “Cat’s Eye”: one connecting the
pinched edges of the minor axis of the core; the other aligned along the core’s major axis.
3.1. Motivations 80
Fig. 3.1. Hubble Space Telescope image of the ‘Cat’s Eye Nebula’: PN NGC6543 – taken by the HST Wide Field Planetary Camera 2. The Image is acomposite of three pictures taken at different wavelengths: red - hydrogen-alphaat 6563 A; blue - neutral oxygen at 6300 A; green - ionised nitrogen at 6584 A:http://chandra.harvard.edu/photo/2001/1220/
3.1. Motivations 81
In terms of fundamental properties, the central star HD 164963 has been classified in
terms of its spectral type as Of-WR (Mendez et al. 1990). This spectral classification is
based three main criteria: a strong and broad emission (FWHM > 4A) in He ii λ 4686; an
Hγ line contaminated with wind emission, particularly in a well developed (or developing)
P Cygni line; the He ii λ 4541 line shows itself to not be in emission, and in the case of
NGC 6543 this is both in absorption and also blue-shifted by ∼ 100 km s−1.
Wesson & Liu (2004) have carried out a temperature-based analysis of the nebula,
mapping the nebula using temperatures derived from ion ratios, while also looking at
temperature fluctuations and ion abundances.
Regarding photometry, a difference in flux of approximately 0.01 mag has been mea-
sured over a period of roughly a year (Bell et al. 1994). In order to try to uncover a
systematic periodicity within the flux, the data were subjected to a time-series analysis
algorithm called PERIOD which ultimately produces a frequency power spectrum from
the Fourier transform of the data. However, each night’s data showed frequency peaks
related to the observation window for that particular night, thereby masking any potential
true periodicity which may have otherwise become apparent. For one night however, JD
2448925, a signal appeared relating to a period of 3.2 h, and when phased to this period,
the data showed some indications of periodicity. Also, for JD 2449282 a signal relation to
a period of 6.2 h was found, but again, this is very close to the observation window. For
the night JD 2449301 a period was found of 2.6 h but this signal was not found in the
data for the other nights. They did not find any signal of the order of 1.45 h as derived
from apparent periodic shifts of the He ii λ 4868, as found by Acker (1976), but NGC 6543
does show photometric behaviour similar to that of a ‘wind variable’ (Mendez 1989).
The variability of the stellar wind of CSPNs is probed further through investigation
into the variations on the shape of P Cygni lines found in UV spectra taken from the short
(UV) wavelength range via the SWP camera on the IUE satellite (Patriarchi & Perinotto
1995): with a sample of 14 objects evidence was found of changing P Cygni shapes in half
the objects, with differences of between 10 – 50% over timescales of years; a parallel is
drawn with wind-based variability seen in population I OB stars, and in the case of NGC
6543, there was also evidence of photometric variation.
Later analysis of additional IUE UV data probes the possibility of variability even
further (Patriarchi & Perinotto 1997). For each object the data is added together and
an average spectrum obtained. Each individual spectrum for a given object is then re-
3.1. Motivations 82
scaled in comparison with the average, and so when studying the resultant data any
differentiation from unity will reveal the presence of possible profile changes, and any
change which is greater than 10% is considered a real change, so changes between adja-
cent spectra can be better analysed and understood. Of particular interest were the regions
containing the more noticable P Cygni lines within the UV range: Nv λλ 1238.82, 1242.80;
O iv λλλ 1338.60, 1342.98, 1343.51; O v λ 1371.29; Si iv λλ 1393.73, 1402.73; C iv λλ 1548.20,
1550.77; N iv λ 1718.55A. The study showed a minimum ±30 km s−1 variation in the blue
edge of the P Cygni profiles. Between 1978 and 1993 they report a 15% photometric
decrease followed by an increase of 10% between 1993 and 1994 for NGC 6543. In terms
of the shape of P Cygni profiles, between 1978 and 1993 there is a 10% decrease in the
emission peak of C iv as well as a 170 km s−1 decrease in its vedge. Between 1993 and
1994 there is an increase of 170 km s−1 of vedge and then again between 1994 and 1995
another 170 km s−1 decrease. In comparing these results with similar variations observed
in population I OB stars, where the observed blue edge shift is of the order of 10% and the
presence of such shifts are attributed to the manifestation of Discrete Absorption Compo-
nents (DACs): are the CSPNs are exhibiting a similar phenomenon, however, they remain
uncertain as they are unable to be sure considering the saturated nature of these CSPN
P Cygni lines.
As regards the intensity variations, there appeared changes of between 10 – 30% across
the entire P Cygni profile, in both absorption and emission; but in OB stars, although
similar levels of variation have been noted in P Cygni lines, the variation has been confined
to the absorption part with the emission peaks remaining constant. The lack of large-scale
continuum variations lends itself to the theory that those observed are due to variations
in the wind (Mendez et al. 1990)
Emission from NGC 6543 has been detected via the Chandra X-ray satellite (see Chu
et al. 2001; Guerrero et al. 2001), both from a point source which would appear to be
the central star, as well as a substantial quantity of diffuse emission; various mechanisms
have been considered by which this diffuse emission could arise. The possibility that the
emission could be produced as a result of the stellar wind interacting with the surrounding
nebula has been negated, as such a model predicts that the emission will peak close to
the inner wall of the interactive region; but for NGC 6543 the diffuse emission appears
to be limited to a more immediate region surrounding the central star. An alternative
idea is that the X-rays are produced by shock-mechanisms originating within the stellar
3.1. Motivations 83
wind itself, that is, similar to shocked systems purported to occur within the stellar winds
of massive O and B stars (Cassinelli et al. 1994); since NGC 6543 does possess a strong
stellar wind (Patriarchi & Perinotto 1991), such a wind-originating shock-mechanism could
so produce X-rays.
The possibility of interaction between a compact object and a close binary companion
is discarded (Guerrero et al. 2001) as the sizes of the objects involved would produce
accretion temperatures of < 105 K for a mass transfer rate of < 10−7 M⊙ yr−1, and this is
too low a temperature for X-ray emission to occur (Pringle 1981). Alternatively, accretive
matter falling directly onto the surface of the compact object could possibly produce X-
rays, and for white dwarfs the velocity of the in-falling material is so high that a shock
develops above the surface of the star: the in-falling material is heated to a temperature
of ∼ 108 K, emitting X-rays. However, the X-ray emission detected from the central
star is too ‘soft’ and does not show the variability associated with high-rate white dwarf
accretion. Therefore the accretion of material from a close companion would appear not
to be responsible for the observer X-ray emission.
Finally, central star coronal activity is considered, (Guerrero et al. 2001): such activity
is caused by the convective and rotational motions of late F-K stars and dMe stars (dwarf
M star exhibiting emission), and also evolved stars going from the late-AGB to a proto-PN
stage may also have convective envelopes. As a star progresses toward becoming a white
dwarf, the ionisation of H and He in its outer envelope ceases at Teff > 30,000 K, but the
central star of NGC 6543 is already a white dwarf, and so this type of coronal activity is
unlikely to occur to produce emission of X-rays; on the other hand, the possibility of a
close binary companion with such coronal activity is not dismissed and the particularly
luminous white dwarf, with L ∼ 5600 L⊙, could possibly out-shine such a F-M dwarf
companion; however, such a companion has yet to be discovered.
In order to uncover some of the basic parameters of the star, the UV and optical
spectra of the star have been modelled with a non-LTE unified model atmosphere code
ISA-WIND (de Koter et al. 1993), and yielded results of effective temperature, Teff , the
helium mass fraction, the terminal velocity of the wind, v∞, the wind acceleration, β, and
the mass flux FM = M /4πR2. The L-to-M ratio is obtained by being proportional to
Teff4/FM
The optical spectrum of NGC 6543 has been modelled from an echelle spectrograph, as
well as HST spectra for the 1150 – 1400 A region, and further UV from an IUE spectrum
3.2. FUSE & Time-Series Data 84
Table 3.1. Preliminary parameters for NGC 6543Parameter Value Reference
Spectral type Of-WR (H-rich) Mendez et al. (1990)Luminosity 5200 L⊙ de Koter et al. (1996)Teff 63000 K Georgiev et al. (2006)Radius 0.6 R⊙ Georgiev et al. (2006)Distance 1001 ± 269 pc Reed et al. (1999)Mass-loss rate ∼ 1 × 10−7 M⊙ yr−1 de Koter et al. (1996)
Georgiev et al. (2006)Terminal velocity 1400 km s−1 This studyWind flushing time ∼ 45 mins This study
(Georgiev et al. 2006). With an adopted luminosity of L = 5200 L⊙ (de Koter et al.
1996), the stellar radius was adjusted until the O iv λλ 1338, 1343, O iv λλ 3560, 3563,
and O v λ 1371 lines were reproduced in the model, in which a clumping factor of 0.1
had been introduced as a typical value for massive stars. The mass-loss rate, M , was
determined from the intensities of H i and He ii optical lines; the terminal velocity is
determined from the blue-ward edges of the UV lines. The best model fit yielded R = 0.6
R⊙, Teff = 63,000 K, M = 0.6 × 10−7 M⊙ yr−1 and v∞ = 1600 km s−1.
Concerning the level of hydrogen deficiency in Wolf-Rayet stars, in particular the
intensity decrement of the Pickering (n → 4) He ii lines, where the lines with an even n
have a similar wavelength to the hydrogen Balmer lines. However the He ii λ 5411 line in
the spectrum is much weaker than either the Hβ or Hα lines and so the star cannot be
hydrogen poor – in consequence it must be hydrogen rich. The iron abundance, determined
in the region 1250 – 1450 A is well reproduced using solar iron abundance, and so would
indicate a level close to the solar value.
In this study fundamental parameters of NGC 6543 have been based upon non-LTE
model atmosphere analysis carried out using the ISA-WIND code (de Koter et al. 1996),
and also CMFGEN (Georgiev et al. 2006).
Fundamental parameters are given in Table 3.1.
3.2 FUSE & Time-Series Data
In order to seek out variability and structure in the fast wind of NGC 6543, (F)UV data
has been obtained from the archive of the Far U ltraviolet Spectroscopic Explorer (FUSE )
satellite.
3.2. FUSE & Time-Series Data 85
Table 3.2. UV/FUV ion speciesIon λ0 [A] log λf Transition El [eV] Eu [eV]
Al iii 1854.716 3.017 2p63s - 2p63p 0.0 6.685Al iii 1862.790 2.716 2p63s - 2p63p 0.0 6.656C iii 977.020 2.872 1s22s2 - 1s22s2p 0.0 12.690C iv 1548.195 2.470 1s22s - 1s22p 0.0 8.008C iv 1550.770 2.169 1s22s - 1s22p 0.0 7.995Nv 1238.821 2.289 1s22s - 1s22p 0.0 10.008Nv 1242.804 1.988 1s22s - 1s22p 0.0 9.976O vi 1031.926 2.137 1s22s - 1s22p 0.0 12.015O vi 1037.617 1.836 1s22s - 1s22p 0.0 11.949P v 1117.977 2.723 2p63s - 2p63p 0.0 11.090P v 1128.008 2.422 2p63s - 2p63p 0.0 10.991S iv 1062.662 1.628 3s23p - 3s3p2 0.0 11.667S iv 1072.973 1.753 3s23p - 3s3p2 0.118 11.673S vi 933.378 2.615 2p63s - 2p63p 0.0 13.283S vi 944.523 2.314 2p63s - 2p63p 0.0 13.127Si iii 1206.500 3.304 2p63s2 - 3s3p 0.0 10.276Si iv 1393.755 2.855 2p63s - 2p63p 0.0 8.896Si iv 1402.770 2.554 2p63s - 2p63p 0.0 8.839
3.2.1 The Instrument Design
The optical design is based upon a Rowland circle: an imaginary circle drawn at a tangent
to the centre of the surface of a diffraction grating, the radius of this circle being half
the radius of curvature of the said grating; if an electromagnetic beam passes through
a slit located somewhere on this imaginary circle then it will strike the grating and be
split, and the consequent beams will be specularly reflected back toward detectors placed
at subsequent focus points located upon the same circle, see Figure 3.2. The Rowland
circle design incorporates four optical paths or channels – co-aligned so that light from
a target object passes through all four simultaneously – each channel consisting of a
mirror, a diffraction grating, a Focal Plane Assembly (FPA) which houses the spectrograph
apertures, and a portion of an FUV detector. The multi-channel design allows the mirrors
and gratings to be coated in such a way as to maximise reflectivity in the wavelength ranges
above and below 1020 A: two mirrors and grating are coated with aluminium with Lithium
Fluoride (LiF) overcoat, which provides twice the reflectivity of SiC at wavelengths > 1050
A but little reflectivity below 1020 A; the other two mirrors and gratings are coated with
Silicon Carbide (SiC) to thus provide a wavelength coverage below 1020 A. The four
channels can be thought to be split onto two sides of the instrument with each side having
3.2. FUSE & Time-Series Data 86
a LiF and a SiC channel, each of which produces a spectrum which falls upon a single
detector. Each channel has a bandpass of ∼ 200 A, so that the information obtained via
two channels, one LiF and one SiC, is needed to cover the ∼ 290 A wavelength range of
the instrument (however all four channels cover the 1015 – 1075 A region).
Fig. 3.2. Diagram depicting the Rowland Circle arrangement of grat-ings and detectors of the FUSE instrument, courtesy of the FUSE website:http://archive.stsci.edu/fuse/instrumenthandbook/
FUSE produces spectra across an overall wavelength range of 905 – 1187 A. The spectra
from the four channels are imaged onto two micro-channel plate detectors, each having one
LiF spectra and one SiC spectra imaged onto it, thereby covering the entire wavelength
range. The two channels are offset perpendicular to the dispersion direction so as not to
allow the spectra to overlap, and also the dispersion direction are opposite for the LiF and
the SiC spectra. Each detector is divided into two functionally independent segments,
A and B, separated by a small gap (∼ 10 A). The detectors are also slightly offset with
respect to each other so that the gap of each does not fall at the same wavelength region
in both detectors. Table 3.3 lists the wavelength coverage of each of the eight detector
segment/channel combination segments, whether detector 1 or 2, LiF or SiC, segment A
or B:
The LiF channels have a dispersive plate scale of 1.12 A mm−1 and the SiC channels
3.2. FUSE & Time-Series Data 87
a scale of 1.03 A mm−1. With the size of the detector pixels this translates to a scale of
∼ 6.7 mA pixel−1 in the LiF channel and ∼ 6.2 mA pixel−1 for the SiC channel – in the
dispersion direction.
Within this thesis, an individual FUSE detector-section combination will be referred
to after the fashion of delineation as given in individual FUSE exposure files: for example,
in reference to an exposure obtained via the lithium fluoride (LiF)-coated detector number
1, section A – this detector-section-combination will be referred to as “1alif”. Therefore,
by example, P v doublet lines are usually analysed via the “2alif” exposures, or otherwise
those of the “1blif” detector-section.
3.2.2 Observing Modes
The two main observing modes used by FUSE are Time Tag (TTAG) or Histogram (HIST)
mode, and each possesses both advantages and disadvantages:
Time Tag (TTAG)
In this mode every photon event recorded by the detectors is sent to the Instrument Data
System (IDS), the computer which records the X and Y coordinates of the event upon the
detector plus the height of the event pulse; but the arrival time of an individual photon
is not recorded. The IDS does not ‘tag’ every photon event – information from all four
detector segments (1A, 1B, 2A, 2B) is sent to the IDS at a maximum rate (for TTAG
mode) of ∼ 8000 events per second – but the IDS inserts time-tags into the data stream
at a nominal rate of once every second, and therefore the (relative) accuracy of photon
arrival time in TTAG mode is 1 second.
The advantages of TTAG mode are that it allows the data to be stored with the full
detector sampling (6 µm in X and 9.1 - 16.3 µm in Y) which provides the highest spectral
resolution to be derived from the data; also data from all apertures is saved and sent
to ground as part of the observation dataset. The efficiency of TTAG memory usage is
seen best with faint targets as most detector pixels do not experience any events during
an exposure; therefore with bright targets the main disadvantage of TTAG is that the
spacecraft solid state recorder has only space for ∼ 120 MBytes of scientific data, and,
for example, a single bright object producing photon events at a rate of 7400 counts s−1
would require ∼ 60 MBytes of data storage space just for a single 2000 second exposure.
The presence of considerable spectral motion on the detector suggests it is preferable
3.2. FUSE & Time-Series Data 88
to make as many observation as possible in TTAG mode. To this end, those observation
with an event rate of < 2500 counts s−1 TTAG is the default mode – similar to a source
producing a flat spectrum of flux ∼ 8× 10−12 erg cm−2 sec−1 A−1. For higher rates HIST
mode is adopted.
Spectral Image or Histogram (HIST)
For an expected count rate of over 2500 counts s−1 the IDS is instructed to bin the data
in its memory in order to produce a spectral image or histogram (HIST), so the time-
tagged facility of TTAG is no longer preserved during exposures; and therefore it is no
longer possible to edit spectral images to remove data obtained during periods of high
background.
One advantage of HIST mode is that higher data rates are supported – the IDS can
process photon event rates up to 32000 events s−1 – similar to a source producing a flat
spectrum of flux ∼ 8× 10−11 erg cm−2 sec−1 A−1 – and very close to the ∼ 1× 10−10 erg
cm−2 sec−1 A−1 brightness limit of FUSE. Unfortunately, at full resolution each detector
segment is 16384 × 1024 pixels in size resulting in spectral images which are 32 MBytes
each – 128 MBytes for all four segments; also, spectral images are built up in the IDS
memory before being sent to the spacecraft recorder and the IDS has only ∼ 35 MBytes
of memory, which means that the IDS cannot store all data/photon events for the whole
detector while in HIST mode; instead only the detector segment containing the spectra
taken through the primary aperture are stored in memory.
However, as a means of combating the degradation of data caused by curvature of an
astigmatic line spread function (the severity of which is not enough to require high fre-
quency sampling in the Y direction i.e perpendicular to the X direction of the dispersion),
the default spectral image mode is to bin the data by a factor of 8 in the Y direction and 1
(no binning) in the X direction, thus reducing the size of the spectral image to < 5 MBytes
per exposure. This binning does not affect the resolution at all for most wavelengths, and
degrades the nominal spectral resolution by only a few percent.
3.2.3 The In-house FUSE Data Reduction Pipeline
Steps undertaken by the FUSE calibration pipeline – taking raw 2D data and processing
it into a set of calibrated 1D spectra – include:
• Data screening (i.e. removing low quality or unreliable data);
3.2. FUSE & Time-Series Data 89
Table 3.3. FUSE channels & FUV spectral sectionsChannel Full Range Gap Section A Section B
A A A A
SiC1 1090.9 - 905.0 1003.7 - 992.7 1090.9 - 1003.7 992.7 - 905.0LiF1 987.1 - 1187.7 1082.3 - 1094.0 987.1 - 1082.3 1094.0 - 1187.7SiC2 916.6 - 1103.8 1005.5 - 1016.4 916.6 - 1005.5 1016.4 - 1103.8LiF2 1181.9 - 979.2 1086.7 - 1075.0 1181.9 - 1086.7 1075.0 - 979.2
Table 3.4. NGC 6543 F034 observationsObs. ID No. exp UT Date MJD (start) ∆t (hours)
F0340105 26 2007-01-13 54113.1260 9.7F0340106 18 2007-01-14 54114.1097 5.9F0340107 19 2007-01-15 54115.0933 7.3F0340108 09 2007-01-16 54116.0680 1.4
• Grating shift correction (i.e. removing spectral motion due to grating motion);
• Drift correction (i.e. calculating image stretch/shift due to thermal effects);
• Background subtraction;
• Flat-field correction;
• Geometric distortion correction (i.e. removing electronic distortions in the delay-line
anode);
• Astigmatism correction (i.e. removing curvature perpendicular to the dispersion
direction);
• Doppler correction;
• Spectral extraction;
• Wavelength calibration;
• Walk correction (i.e. correcting for pulse-height-dependent errors in the photon
location);
• Dead-time correction;
• Flux calibration (counts s−1 into erg cm−2 s−1 A−1);
• Channel co-addition (for simple visual analysis).
3.2.4 The FUSE Time-series Data of NGC 6543
The time-series analyses presented in this chapter are based upon FUSE data from program
F034 (PI – DL Massa) obtained between 13th – 16th January 2007, the details of the
observations are listed in Table 3.4.
3.2. FUSE & Time-Series Data 90
Despite some light lost while using the medium resolution (MDRS) aperture 4◦ × 20◦,
a total of 72 exposures were taken, and their distribution over the four nights is detailed
in Table 3.4. Of these 72, there are 59 adequately captured via the Lif2 channel (segment
A: wavelengths 1086 – 1182 A), where the P v λλ 1117.98, 1128.01 is located. Other data
from the LiF1 channel (segment A: wavelengths 987 – 1082 A) giving information on the
saturated O vi λλ 1031.92, 1037.62. Some limited data – not all FUSE sections managed
to obtain sufficient starlight data in all epochs – is also available in the SiC 2 channel
(segment A – wavelengths 917 - 1006 A), namely S vi λλ 933.38, 944.52
The mean spectrum for NGC 6543 – F034 (Figure 3.5) provides strong P-Cygni profiles
in a number of lines aside from the aforementioned Pv , O vi and S vi resonance lines. A
possible blueward absorption is shown in the N iv λ 955.34 line and also in C iii λ 1175.67.
Apart from the stellar wind-formed lines the spectrum is dominated by narrow inter-
stellar and circumsystem absorptions lines due to atomic species and molecular hydrogen.
Also the blue O vi λ 1031.92 component of the doublet is affected by a sharp emission spike
from the Ly-β line.
Ionisation details of all UV resonance lines investigated in various degrees in this and
the following two chapters are given in Table 3.2.
3.2
.FU
SE
&T
ime-S
eriesD
ata
91
Fig. 3.3. ‘Exploded-view’ diagram of the FUSE instrument showing the spatial relationships between its mirrors, gratingsand detectors; courtesy of the FUSE website: http://archive.stsci.edu/fuse/instrumenthandbook/
3.2. FUSE & Time-Series Data 92
Fig. 3.4. Diagram of the four FUSE detectors indicating their wavelength-dependent arrangement of lithium fluoride and silicon carbide coatings, also cour-tesy of the FUSE website: http://archive.stsci.edu/fuse/instrumenthandbook/
Fig. 3.5. Mean FUSE spectrum of the central star in NGC 6543 taken from theF034 run in January 2007.
3.3. Evidence of Variability 93
3.3 Evidence of Variability
Of the wind lines present within the spectral range afforded by the FUSE data, the P v
line appears as a well-developed but crucially un-saturated P Cygni profile, and therefore
will prove to be the primary diagnostic of the fast wind’s physical parameters as well as
the prime demonstrator of its variability.
Fig. 3.6. The maximum fluctuation in the P v λ 1117.98 resonance line comparedwith the more stable low velocity regions of O vi λ 1037.62.
The optically-thick O vi shows minimal variation, but Pv shows definite signs of
significant variability, the most significant of which occurs between ∼ − 500 and − 1300
km s−1 in the blue component, λ0 = 1117.98 A; the red component show variability above
the 95 % confidence line bewteen −250 and −1375 km s−1. λ0 = 1128.01 A. The equivalent
width of the line is not conserved and varies from as low as ∼ 0.3 to ∼1.7 A, giving a mean
equivalent width of ∼0.8 A (s.d. of ∼0.8 A), as measured between 1110.5 and 1121.8 A in
the blueward part of the Pv doublet, that is to say a variation of ∼120%; likewise in the
red component the EW also fluctuates, the absorption trough varying between 1.13 and
1.83 A (mean of 1.47 A, s.d. of 0.12 A), the strong emission peak varying between 0.48
and 1.85 A ( a mean of 0.99 A, s.d. 0.22 A).
3.3. Evidence of Variability 94
In contrast, the TVS spectrum of the O vi line shows little temporal activity, and the
regions wherein P v shows the greatest variance, in O vi the fluctuations in the absorption
are minimal at best, with the equivalents widths ranging between ∼8.7 to ∼10.7 A with
a mean of ∼10.2 A (and s.d. of ∼0.4 A) as measured between 1021.2 and 1037.2 A,
indicating a variation of no more than 15%, merely an eighth of the variability of the Pv
resonance line, and would be difficult to quantify due to the highly saturated nature of
the absorption.
The application of TVS to time-series of select absorption lines provides further ev-
idence of which of the wind lines possess the greater variability and therefore warrant
further investigation. The result of such an analysis are presented below.
6.0
8.0
10.0
12.0
14.0
16.0
18.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.4
0.6
0.8
1.0
1.2
1.4
Flu
x
5.0
10.0
15.0
20.0
25.0
30.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0 1000 2000Velocity (km/s)
0.5
1.0
1.5
2.0
Flu
x
Fig. 3.7. Time Variance Spectra (TVS) of the two most developed P Cygniabsorption doublets from the F034 time-series spectra: the well-developed butunsaturated P v λλ 1117.98,1128.01 doublet (left) is clearly strongly variableacross both the blue and red absorption troughs of the doublet, showing broadpeaks above the dotted 95% confidence line; in contrast, the highly saturatedO vi λλ 1032.97,1038.93 doublet (right) shows a negligible TVS response
3.3. Evidence of Variability 95
Fig. 3.8. Greyscale images of the four nights’ optical spectra (2alif section) fromthe F034 observation. These are displayed left to right and bottom to top as thethe individual greyscale images chronologically proceed from the bottom of theimage upwards: 13th, 14th January shown bottom left, right; 15th, 16th Januaryshown top left, right.
3.3. Evidence of Variability 96
Fig. 3.9. A single greyscale image of the 2alif section spectra of the entire F034data. Using this singular format, it is easier to observe the cyclic behaviour ofthe DACs present in the P v doublet.
3.3. Evidence of Variability 97
3.3.1 Discrete Absorption Components
Discrete Absorption Components – referred to throughout this thesis and in the literature
as DACs – are regions within the confines of an absorption trough of a stellar wind P
Cygni line profile and are often found in the spectra of OB stars (Fullerton et al. 2006b)
where there is a localised enhancement of the optical depth. Through time-series analysis
these can be seen to migrate within the resonance line, slowly accelerating with regards
to the flow of the wind.
It has been observed in a number of studies of time-series spectra from OB stars that –
within the absorption trough of a given P Cygni profile – an ‘additional’ absorption feature
appears at ∼ 0.5 v∞but has been observed to appear at ≤ 0.3 v∞ (Prinja et al. 2002).
This feature then migrates blueward over several hours or days through the absorption
trough, narrowing (in velocity width) as it does so (Cranmer & Owocki 1996). It has also
been suggested through further study of time-series IUE data that a connection existed
between the periodic appearance of these features and their acceleration and the projected
rotation velocity of the star, vesin(i) (Prinja 1988).
For an expanding wind the radial optical depth at any position is given by the Sobolev
approximation:
τrad(v) ∝ qiρ
(
dv
dr
)−1
(3.1)
(Fullerton et al. 2006b)
These enhancements can be achieved by increasing the local ionisation fraction, qi, in-
creasing the local wind density, ρ, or by reducing – flattening – the local velocity gradient,
dv/dr, or by a combination of these inter-related factors.
Using time series spectra taken by the FUSE satellite the appearance of DACs can
be observed and the behaviour of different DACs appearing with the resonance profiles of
different ions can be studied. It can be shown through time-series greyscale images that
the appearances of the DACs repeat in a cyclic manner with a recurrence period of the
order of rotation, and in studies of ion doublets, e.g. Pv and S iv , the recurrences are in
phase. It has also been noted that, as well as in the resonance profiles of the dominant
ions, DACs also appear in the profiles of adjacent ions (e.g. P iv , S iv , S vi ), and also in
trace ions such as O vi .
3.3. Evidence of Variability 98
However, the DAC amplitudes are weaker in the dominant ions and stronger in the
profiles of weaker species. This discrepancy in strength between the dominant and less so
species would seem to indicate that the velocity gradient cannot be seen as the main cause
of the occurrence of DACs, nor can local density enhancements. Also since the DACs can
be seen to propagate in phase between different ionisation stages: dominant, weaker, or
even in super ions (e.g. S iv , S vi ), this would suggest that changes in ionisation levels
again cannot be the sole cause of their appearance.
Therefore, instead of the cause being any single parameter of the radial optical depth,
τrad(v), a DAC’s occurrence must be due to a combination of the different factors.
Such a mechanism could be a localised flattening of the velocity gradient, as has
been observed via hydrodynamic modelling of Co-Rotating Interaction Regions (CIRs)
(Cranmer & Owocki 1996), caused initially by localised increases, or decreases, in the
radiative force resulting in a bright, or dark, spot near a star’s equator. Bright spots
generate high-density but slow moving streams, and dark spots provide lower-density
but fast moving streams. The CIRs are produced when faster moving material catches
up with slower moving material: the leading edge of a fast-moving streams catches up
with a slower moving stream, the interaction between the two may steepen into a shocked
region. The unperturbed super sonic wind then obliquely impacts upon the CIR, resulting
in a “sharp propagating discontinuity” (C & O 1996): a plateau, and where there is a
flattening of the velocity gradient there is also an increase in density at similar velocities,
but different spatial locations. The fluctuations in density combined with changes in dv/dr
result in small variations in the absorption profiles of excited transitions and dominant
ions. However, as recombination preferentially increases the abundance of lower ions then
DACs are fractionally stronger within them.
A method, somewhat akin to that used by Patriarchi & Perinotto (1997), can be
utilised in order to better locate and measure the progression of the DACs as they move
through the wind. For each spectral sequence a mean spectrum is created and then this
mean is divided into each of the individual spectra in that particular sequence. The aim
of this procedure is to produce a second sequence of mean-rectified spectra in which all
deviations from the continuum value of unity denote regions where there is a significant
deviation from the mean: in this way the appearance of a DAC will be highlighted by a
region lower than the continuum, and which, as the sequence progresses, will move further
left just as the DAC will travel blueward in the UV time-series spectra as it moves outward
3.3. Evidence of Variability 99
through the wind.
Fig. 3.10. A pair of multi-stacked mean-rectified spectra showing the velocity-space fluctuations from the mean 2alif spectra of the two DAC sequences – thismethod allows for easier identification of the progression of the DACs through thesequences. The central velocity of each individual blueward DAC is marked witha red tick – this is the position of the individual velocity measurements taken inorder to estimate the acceleration of the DAC through the wind.
In Figure 3.10 the two mean-rectified sequences are shown and the progressions of the
two significant absorption regions, one in each sequence, and denoted by a red tick mark
where the central velocity of each sequential DAC has been estimated. The subsequent
velocity measurements can be combined with each corresponding Julian date as set of data
coordinates of centralised velocity vs. time, which can then be plotted. The coordinates
can also be entered into a least-squares algorithm which will calculate the gradient and
y-axis intercept for a least-squares fit through the plotted data – the gradient therefore
representing an approximation of the average acceleration of the DAC through the narrow
velocity range of its appearance in the greyscale images as it moves through the stellar
3.3. Evidence of Variability 100
Fig. 3.11. Plotted progressive velocity tracks of two DAC sequences, each over-plotted with a least-squares fit of the resultant acceleration.
wind. The first sequence, taken from the first night’s data, indicates an acceleration of
approximately 3 × 10−3 km s−2; the second sequence, taken from the second night’s data,
indicating an acceleration of approximately 8 × 10−3 km s−2. The error margin for both
is ∼ 10%.
3.4. Modulated or Cyclical Behaviour 101
3.4 Modulated or Cyclical Behaviour
The behaviour of DACs in OB stars has been demonstrated in several case studies (Massa
et al. 1995; Kaper et al. 1996; Fullerton et al. 1997; de Jong et al. 2001; Prinja et al. 2002):
these are modulated and may related to the rotation period of the stellar wind source
star. A similar study of wind variability is therefore of interest in that emanating from the
central star of NGC 6543. In particular the optical depth changes, as mentioned above in
terms of maximum and minimum values, may also exhibit a cyclic behaviour.
In order to try to uncover any inherent cyclic behaviour the time-series spectra are
submitted to a Fourier-based periodogram analysis to uncover the quantitative nature of
any repetitive behaviour. The Fourier method involved utilises the CLEAN algorithm
(Roberts et al. 1987), as described in Chapter 2, to diminish false frequency signatures as
might evolve from the underlying noise, as well as aiming to eliminate as much as possible
the window function – the duration period of the nightly observations which, due to the
repetitive nature of the observing run, might imprint itself upon the resultant frequency
power spectrum.
To this end a gain of 0.5 over 200 iterations was undertaken of a select velocity range
of the time-series, in the blueward wind velocity between −600 to −1100 km s−1 which
is approximately the extent of the range of the selected DACs as seen in the greyscale
images.
The resulting power spectrum shows a number of peaks across a frequencies range
of between 0 and the maximum frequency (as inputted as a parameter in the Fourier
algorithm) of 20 cycles per day – see Figure 3.12. However there appears a strong power
peak at 5.8125 cycles per day – corresponding to a period of ∼ 0.172 d, or ∼ 4.129 h (4
hours 8 minutes) – see Figure 3.13. A subsequent greyscale image of the P v wavelength
ranged, phased to a period of 0.172 d illustrates this repetitive modulation over three
cycles, and this is shown in Figure 3.14. There does appear to be some coherence between
this period value and the DAC progression within the wind across the estimated range of
−600 to −1400 km s−1.
IUE data, which is the following section provides a measure of the terminal wind
velocity for the SEI line profile fitting programme, can also be used as an alternative
source of evidence of line variability, given a sufficient number of exposures. Taking low
resolution IUE spectra – where R ∼ 300 – from the ESA archive, where a sequence of 39
3.5. Line Synthesis & Optical Depths 102
−1000 −900 −800 −700Velocity (km/s)
0.4
0.5
0.6
0.7
0.8
Flu
x
0 2 4 6 8Power x 10−4
0
5
10
15
201.1
1.8
2.5
3.2
Pow
er x
10−
4
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
−1000 −900 −800 −700Velocity (km/s)
0.4
0.5
0.6
0.7
0.8
Flu
x
0.5 1.0 1.5 2.0Power x 10−4
0
5
10
15
200.8
2.3
3.7
5.2
Pow
er x
10−
5
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
0
5
10
15
20
Fre
quen
cy (
cycl
es p
er d
ay)
Fig. 3.12. Full-panel displays of Fourier-based frequency analysis of the bluetrough of the P v doublet, as seen in the F034 spectra, analysed between −600 –−1100 km s−1, with the ‘dirty’ analysis on the left, and the ‘clean’ analysis (gain= 0.500) on the right.
exposures, SWP54865 to SWP54961, taken over 4.2 days, these spectra show a significant
level of variability in the blue wing of the C iv line, even though the line is quite saturated.
The variance of the C iv line is shown in Figure 3.15, and there appears to be something
of a double peak in the TVS of the absorption part of the P Cygni profile as well as a
third peak on the red emission side. Taking the range −1000 – −2000 km s−1 as probably
covering the fluctuations in the extreme blue edge of the absorption, the 39 spectra are
passed through the time-series Fourier (CLEAN) analysis to try an uncover an underlying
periodicity in the variance.
3.5 Line Synthesis & Optical Depths
The physical properties of the DACs present within a stellar wind can be estimated through
the use of the SEI absorption profile modelling method. As detailed in Chapter 2, the
radial optical depth of the profile is treated as 21 independent velocity bins (each ∼ 0.05
v∞ wide) in order to provide a flexible means by which to match absorption optical depths
3.5. Line Synthesis & Optical Depths 103
Fig. 3.13. Extracted power spectrum output of a Fourier-based frequency anal-ysis of the F034 spectra, analysed between −600 to −1000 km s−1(the velocityrange across which the DACs appear to traverse): the top panel shows the powerspectra derived from the ‘dirty’ analysis in black, with the ‘cleaned’ analysis (gain= 0.500) superimposed in red; the bottom panel shows the cleaned analysis onits own in red, with the highest peak indicating a strongest signal occurring at ∼5.8125 cycles per day.
in a structured wind affected by variable features such a DACs. The method assumes a
standard parametrised velocity law:
w = w0 + (1 − w0)(1 − 1/x)β (3.2)
where w = v/v∞ and x = r/R⋆ i.e. the parametrised wind velocity and radial distance.
The presence of the initial photospheric spectrum in the SEI profile is approximated
by a Gaussian of FWHM = 200 km s−1: this has the effect of improving the line fit at the
lower radial velocity end (≤ 0.2 v∞) of the absorption profile under investigation, here Pv .
The dimensions of the input photospheric Gaussian, for the specific ion being modelled in
SEI, are derived from the corresponding photospheric line profile taken from the a specific
3.5. Line Synthesis & Optical Depths 104
Fig. 3.14. Greyscale representation of the F034 P v doublet folded over a periodof 0.172 days – here displayed over three cycles.
photospheric spectrum chosen from the TLUSTY model grid; the specific spectrum chosen
for the parameters of Teff and log g closest to those of the object being modelled, in this
case NGC 6543, for which the grid spectrum for Teff= 55,000 K and log g = 4.00 is chosen
as being the closest approximate photospheric model for the corresponding parameters of
NGC 6543: Teff = 63,000 K, log g = 4.2 (Georgiev et al. 2006). The chosen TLUSTY
grid model spectrum is then fed into a simple algorithm, ROTIN3, which rotationally-
broadens a user-specified wavelength range about the central wavelength of ion intended for
modelling (e.g. P v λ 1118); the subsequent rotationally broadened range is then outputted
as a simple ASCII file which can then be fed into DIPSO, and thence the optical depth
and velocity FWHM can be measured and these dimensions then applied as the SEI
photospheric input parameters.
The model fit for the mean P v profile is shown to have a very good fit with parameters:
3.5. Line Synthesis & Optical Depths 105
5.0
10.0
15.0
20.0
(TV
S)1/
2 (%
FC)
−4000 −2000 0 2000 4000Velocity (km/s)
0.5
1.0
1.5
2.0
Flu
x
Fig. 3.15. TVS analysis of IUE data of the C iv λλ 1548, 1550 doublet – notethe double/triple nature of the variability response.
v∞= 1400 km s−1, and vturb (the small scale (turbulent) velocity dispersion parameter) =
0.05. Although an earlier SEI modelling had been undertaken with a velocity acceleration
factor of β = 1.0 (Prinja et al. 2007), in the modelling undertaken for this thesis it was
found that a revised factor of β = 1.25 provided a better overall fit, while not necessarily
making much difference to the absorption profile fit, the increased factor gave a better fit
to the redward emission part of the profile.
The values derived for the average Mq(P4+) – measured between 0.2 and 0.9 v∞ –
for the mean spectra of each night of the observing run, as well as an overall ‘average’
measure, for the entire observation, are listed in Table 3.5.
It should be noted however that the SEI modelling code assumes a spherically-symmetric
wind, and as such, the models often predict excess forward-scattered emission in the low
velocity part of the absorption trough, that is below 0.25v∞, and so, for NGC 6543 with
v∞= 1400 km s−1, the model fit below ∼ 350 km s−1 cannot be relied upon. This excessive
prediction is inherent in the code as one attempts to model higher velocity absorption by
increasing the optical depth, thereby reducing the transmitted flux of the more blueward
velocity bins; then the model compensates by increasing the forward scattered component
3.5. Line Synthesis & Optical Depths 106
Fig. 3.16. SEI fits to the mean P v resonance profiles of the 4 consecutive nightsof the F034 run: 13th, 14th January 2007, top left, right; 15th, 16th January 2007,bottom left, right.
at lower velocities (Massa et al. 2003). There may come a time when the model thereby
predicts more scattered light than is observed in the spectrum, then even if one attempts
to increase the optical depths of the lower velocity bins – even by some arbitrarily large
optical depths far greater than those assigned to the higher velocity end – the low-velocity
part of the profile will not deepen. Unfortunately the scale of the excess scattering has a
correlation with the line strength and so is prevalent in deeper absorption lines, particu-
larly strongly saturated ones. A readjustment of depth and FWHM width of the inputted
photospheric ion profile may be attempted, but then there is the risk of introducing di-
mensions which cannot be adequately wind-rectified in the subsequent P Cygni profile.
Therefore the validity of the SEI model assumptions has to be questioned, particularly the
fundamental assumption of a spherically symmetrical wind and its apparent homogeneity
(Massa et al. 2003).
3.5. Line Synthesis & Optical Depths 107
Fig. 3.17. SEI model fit of the mean spectrum from the F034 observation.
As well as the spherically symmetric models predicting too much low velocity scatter-
ing, the inability of the model to match the shape of the observed profile may reflect an
unaccounted-for ‘clumpiness’ in the wind. An inhomogeneous, ‘clumped’ wind would lead
to the derivation of low ionisation fractions – such as those obtained for B supergiants
(Prinja et al. 2002). Also, if the wind if actually composed of dense clumped regions sep-
arated by less dense spaces, then each constant velocity surface will not fully contribute
to the emission, and similarly the surface of the star will not be completely covered by
optically thick material: in fact it would be relatively porous. This would lead to the
absorption regions would not be very deep – appearing less deep than in reality – thus
appearing less saturated than they should. When fitting the apparent absorption profile,
the optical depths, and subsequent Mq values assumed, would not be optically as deep as
if the wind was homogeneous (Oskinova et al. 2007).
3.5. Line Synthesis & Optical Depths 108
Table 3.5. NGC 6543 F034 Mq resultsObs. ID UT Date MJD (start) Minimum Maximum Av.(0.2 – 0.9v∞)
M⊙ yr−1 M⊙ yr−1 M⊙ yr−1
05 2007-01-13 54113.1260 1.1e-09 1.2e-08 5.5e-0906 2007-01-14 54114.1097 1.4e-09 1.5e-08 5.9e-0907 2007-01-15 54115.0933 1.3e-09 1.2e-08 5.8e-0908 2007-01-16 54116.0680 1.8e-09 1.3e-08 5.3e-09Mean – – 9.0e-10 1.3e-08 5.5e-09
3.5.1 Errors Inherent in SEI Mqi(w) Calculations
As detailed in Chapter 2, the SEI code calculates a velocity dependent mass-loss rate-
ionisation fraction product, Mq(w), as well as also providing an average Mq figure as
integrated between 0.2 and 0.9 of the normalised velocity function, w, thus:
M qi(w) =mec
πe2
4πµmH
fλ0AER⋆v
2∞x2w
dw
dxτrad(w), (3.3)
and therefore, in simplifying the above equation the Mq value obtained can be simply
expressed as a proportionality relation with the essential parameters used by SEI in order
to calculate the Mq, thus:
M qi(w) ∝ R⋆v2∞
dw
dxτrad(w), (3.4)
Temperature of stars are usually given to the nearest thousand degrees Kelvin and
so, with temperatures ranging between ∼ 30,000 and ∼ 45,000 K, the largest fractional
error margin can be approximated to 1000/30000 i.e ∼3%; similarly error margins of
luminosity can be estimated at being around the 10% mark. Therefore in combining the
error fractions of both luminosity and temperature to derive an error for stellar radius,
the resulting percentage error for the stellar radius is ∼6%. The terminal velocity as
measured via the blue edge of staurated P Cygni profiles can be derived to within ±50
km s−1, therefore for wind speeds in the range of −500 – −1500 km s−1 the greatest error
margin is of the order of 10%.
As well as these error margin estimates of the SEI code input parameters, there are also
3.5. Line Synthesis & Optical Depths 109
the more manually-based errors of manipulation inherent in the modelling of the profiles
themselves.
The error calculation corresponding to the simpler proportionality relation of Mq given
above in Equation 3.4, is as follows:
(
∆Mq
Mq
)2
=
(
∆R⋆
R⋆
)2
+ 2
(
∆v∞v∞
)2
+
(
∆β
β
)2
+
(
∆τrad
τrad
)2
(3.5)
where the error in the stellar radius, ∆R⋆, is derived from the errors of L and Teff , as SEI
uses the input parameters of luminosity and stellar effective temperature to calculate the
subsequent stellar radius. From the stellar luminosity-temperature relationship:
L⋆ = 4πR⋆2σTeff
4 ⇐⇒ R⋆ =√
(L⋆/(4πσTeff4)) (3.6)
and hence the subsequent error in the stellar radius can be derived:
(
∆R⋆
R⋆
)2
=1
2
[
(
∆L⋆
L⋆
)2
+ 4
(
∆Teff
Teff
)2]
(3.7)
As the SEI modelling procedure is able to match the overall morphology of the P v ab-
sorption profile, through the normalised velocity bin-by-bin adjustment of optical depths,
it therefore allows one to model profiles from individual exposures. Consequently, it has
been possible to match the P v absorption profiles for a couple of sequences of individ-
ual spectra from the F034 dataset, namely the spectra of exposures F03401050012 to
F03401050082 (1st night) and from F03401060042 to F03401060122 (2nd night): these se-
quences correspond to the appearance and migration of the DAC-like features as shown
in the lower panels of Figure 3.16. The variation in the fits to these spectra is due to the
occurrences of DACs, and therefore can be compared to a non-DAC spectrum (such as the
profile of F03401080072) which provides a representation of a maximum flux/minimum
absorption over most velocities (i.e. between 0.0 and 1.0 v∞).
The SEI fits to these two spectral sequences are shown in Figure 3.18 where it is ably
depicted that the manipulation of the individual velocity bin’s optical depth, in order to
match the varying morphology of an absorption profile as it were frame by frame, is a
3.5. Line Synthesis & Optical Depths 110
excellent means by which one can demonstrate that the wind profiles of CSPNs (as with
OB stars) can be structurally distorted by such DAC-like features migrating through the
wind.
Fig. 3.18. A pair of multi-stacked spectra showing the velocity-space progressionof P v doublet DACs for two sequences.
From these SEI model sequences one is then able to extract optical depths at specific
velocity of these migrating DACs (as described in Section 3.3, and illustrated in Figures
3.8 and 3.9), and therefore examine the variation and progress through the wind of optical
depth features at their migrating central velocities. These central velocity-localised DAC
3.5. Line Synthesis & Optical Depths 111
optical depths can also be ‘normalised’ by dividing each within the sequence by the corre-
sponding optical depth in the non-DAC case. The resulting ratios of τDAC/τmin from the
two sequences can be plotted as a function of normalised velocity, w, as illustrated in Fig-
ure 3.19. This plot shows how the optical depth ratio for the two independent sequences
develops as the DACs move through the wind. In each case the ratio increases from ∼1.5
to a maximum of ∼4.0 at around 0.6 v∞ and then drops down to ∼1.0 at around 0.7 v∞.
It them seemingly begins to increase a second time toward 0.8 v∞ before the DAC(s) fade
out.
Fig. 3.19. Plot showing the changes of the radial optical depth ratios,τDAC/τmin, for the two DAC sequences.
3.5.2 The Case for Clumping via CMFGEN
A better insight into the effects of a clumpier structure to the wind can be gained via
the unified atmosphere code CMFGEN (Hillier & Miller 1998), which calculates non-LTE
models of the entire stellar atmosphere from the photosphere right out to the extremities
of the outflow of spherically-symmetric winds with multi-level ions.
Whereas TLUSTY assumes plane-parallel geometry in order to provide an accurate
model of a fully line-blanketed photosphere, CMFGEN employs spherical-symmetry in
order to extend the nLTE line-blanketed atmosphere into the stellar wind beyond. This
unified-wind-atmosphere code was written by Hillier (1990) and later developed by Hillier
& Miller (1998) whereupon the effects of iron species line blanketing were applied to the
3.5. Line Synthesis & Optical Depths 112
original 1990 code.
The prime directive of the code is the solving of the radiative transfer equation for
stars with a spherically-extended atmosphere outflow using the Sobolev approximation or
the full solution of the co-moving-frame radiative transfer equation. The original iteration
code takes a tridiagonal Newton-Raphson operator, which is based upon the complete lin-
earisation method forwarded by Auer & Mihalas (1969), but without limitation upon the
number of energy level transition it is able to deal with. In essence, a partial linearisation
method is employed, not unlike that of the approximate lambda operator as seen in the
TLUSTY methodology, with similar convergence. Like TLUSTY, the ultimate aim is the
inclusion of a many blanketing lines as possible in the model while at the same time reduc-
ing the computations involved to a minimum; again as with the iterative TLUSTY lambda
operators, radiative transfer in the lines is treated ‘exactly’ as no opacity redistribution
or sampling techniques are used.
While extending the radiative transfer equation solutions into line-blanketing, the con-
cept of (Anderson’s) superlevels reduces the number of energy levels that need to be solved
explicitly.
The populations of the superlevel Sn are include in the solution of the rate equations;
the population of an individual atomic level in the full model atom F n but which possess
similar departure coefficients as their ‘parent’ superlevel.
F∑
i
nij =S nj (3.8)
F∑
n∗
ij =S n∗
j (3.9)
where * denotes LTE population, Snj is the population density of superlevel j and F nij
is the population density of the full level i which is a member of the superlevel j.
b =F nij
F n∗
ij
=Snj
Sn∗
j
(3.10)
The linearisations are performed by replacing F nij by:
3.5. Line Synthesis & Optical Depths 113
F nij =S nj
(
F n∗
ij
Sn∗
j
)
(3.11)
Here, F nij is temperature-dependent as it depends upon F n∗
ij/Sn∗
j . Also using super-
levels in this way extends LTE which assumes a single superlevel to describe all ionisation
stages; in an nTLE environment each ionisation stage is represented by many levels.
However, in order to avoid the innumerable lines overlapping and merging near series
limits, one of the improvements to the original 1990 code includes an approach similar to
that of Hubeny et al. (1994) – adopting an occupation formalism probability of Hummer &
Mihalas (1988) – is used, along with other opacity redistribution functions. The approach
is the defining of a level occupation probability of wi and that of a higher level is wj : for
transitions between state i and j the occupation probability for state j is assumed to be
wj/wi as state i is undissolved; but if state i is dissolved then the occupation probability
of state j goes to zero – this is because if the lower energy state is to be dissolved then
the higher state must be also being closer to the continuum.
Other enhancements to the 1990 code include dealing with potential resonances in
photo-ionisation cross sections, as well as the effects of such as regards Auger ionisations
(see Hillier & Miller 1998 for details).
The code was run by Miguel Urbaneja (of the Institute for Astronomy, Hawai’i –
obtained via private communication), using the fundamental parameters as listed in Table
3.1, with the addition of log g = 4.2 and a He/H abundance ratio of 0.1 (e.g. Georgiev et al.
2006). A parametric treatment of wind clumping form part of the CMFGEN modelling:
this is calculated via a volume filling factor f , defined as:
f = f∞ + (1 − f∞)exp(−v/vcl), (3.12)
where vcl is the velocity at which clumping starts – adopted as 35 km s−1 – above the sonic
point. Although CMFGEN can be used to model the entire stellar atmosphere, the main
issue for this investigation was to see the effects of clumping in CMFGEN models upon
the fast wind of NGC 6543; and so fittings were limited to a few key lines and not the
entire atmospheric spectra.
3.5. Line Synthesis & Optical Depths 114
Fig. 3.20. CMFGEN model fits of key diagnostic lines for NGC 6543 are shown(from FUSE and high-resolution IUE spectra), where the superimposed modelshave filling-factors of f∞ = 0.06 (solid line), 0.08 (dashed line), and 0.10 (dottedline). Courtesy of Miguel Urbaneja (via private communication).
A selection of models have been run with varying volume filling – “clumping” – factors,
with f∞ = 0.06, 0.08 and 0.10, and the resultant synthesised spectra then compared to
a few key line profiles as detailed in FUSE and high-resolution IUE data of the central
star, as shown in Figure 3.20. Taking a mass-loss rate of 6 × 10−8M⊙ yr−1, the models
show good overall fits to the observed resonance and excited line profiles, with the P v
line more sensitive to clumping factor than O v and N iv . The best-fit case is for the
filling factor of f∞ = 0.08 but this is based upon (F)UV line fitting only and does not
incorporate diagnostic optical lines for the central star of NGC 6543 such as He ii λ 4686
or C iv λ 5801.
In Figure 3.21 the ionisation fraction of the P 3+ P 4+ and P 5+ ion species are displayed
as function of wind velocity for each of the three clumping factors. It can be seen that
the ion fraction of P 5+ shows a dominance at low velocities, and it is this dominance
which results in the lower velocity mis-match of the model for the P v resonance line.
3.6. Conclusion 115
Fig. 3.21. Log plots of the P iv , P v and P vi ion fractions as functions of theblueward wind velocity, for the filling-factor cases of f∞ = 0.06 (solid line), 0.08(dashed line), and 0.10 (dotted line). Courtesy of Miguel Urbaneja (via privatecommunication).
Although not dominant, the ion fraction of P 3+ and P 4+ both increase with velocity
across all velocities with evidence of recombination from P 5+ to P 4+ at the approach to
the terminal wind velocity.
Other CMFGEN models predict that the dominant ions are those of C4+ and P 5+ –
i.e. qi > 0.97 over ∼ 0.2 to 0.9 v∞ and S5+ and O4+ close to a dominant level – 0.6 and
0.2 respectively.
P v is therefore sensitive of small-scale clumping in the fast wind, coupled with the
presence of larger scale structures as evident with the appearance of the DACs.
3.6 Conclusion
In this chapter evidence has been found in the FUSE UV data of NGC 6543 that the
outflow emanating from its central star is variable on a time-scale of hours; also this vari-
ability is attributable to the appearance of recurrent additional optical depth absorption
features which are seen to migrate blueward through the absorption troughs of the UV P
Cygni profiles. In depicting such temporal behaviour in the profile of the P v resonance
3.6. Conclusion 116
Table 3.6. Comparison of NGC 6543 and mid O-star properties
DAC measure NGC 6543 O stars (e.g. O7 III)
vinitial ∼ 0.3 v∞ ≤ 0.3 v∞Recurrence yes (over ∼ hours) yes (over ∼ days)(dv/dt) × (R⋆/v∞) ∼ 12–24 km s−1 ∼ 10 km s−1
maximum τ(DAC)/τ(min) ∼ 4 ∼ 5Quasi-periodic yes; P ∼ 0.14 days yes; P ∼ daysFWHM/v∞(initial) ∼ 0.15 v∞ ∼ 0.3 v∞FWHM/v∞(final) ≤ 0.05 v∞ ≤ 0.1 v∞
lines of NGC 6543, it has been observed that such behaviour is similar to that exhibited by
the presence of DACs in UV data of hot, luminous OB stars. In comparing the ‘DAC-like’
properties of NGC 6543, as seen in this study, to those formerly observed in various studies
of OB stars (e.g. Kaper et al. 1996; Prinja 1998; Fullerton et al. 2006b), it is noted that
such parameters are remarkably similar for the two different stellar systems: these are
compared in Table 3.6. In terms of the initial DAC detection within the absorption profile
is similar for the two. Although it is noted that the velocity dispersion of the two DAC-
type structures differ in that the approximate FWHM velocity measurements of the DACs
of NGC 6543, which range between ∼0.15 v∞ at their initial appearance before narrowing
to ∼0.05 v∞ or less as they migrate, are half the width of the similar measurement for
O stars (initially at ∼0.3 v∞ and then narrowing to ∼0.1 v∞ with migration); conversely
the flow-time-scaled linear accelerations for NGC 6543 (which must be taken as estimated
‘average’ values because of the velocity-law dependence of the model acceleration of the
wind), are perhaps, at the higher measure of ∼26 km s−1, as much as double the similarly-
scaled acceleration of O stars, at ∼10 km s−1. Despite these immediate differences, the
velocity dispersions and the estimated (linear) accelerations, are of the same order for
NGC 6543 and O stars.
It has been suggested that the appearance of DAC structures in the stellar wind and
their quasi-periodic behaviour is a manifestation effect of Co-Rotating Interaction Regions
(CIRs) (Cranmer & Owocki 1996), which are instigated by localised increases (bright
spots) and decreases (dark spots) in a star’s equatorial radiative force. Bright spots
generate high-density but slow moving streams, and dark spots provide lower-density but
fast moving streams. The CIRs are produced when faster moving material catches up
with slower moving material: the leading edge of a fast-moving streams catches up with a
slower moving stream, the interaction between the two may steepen into a shocked region.
3.6. Conclusion 117
Then unperturbed super sonic wind then obliquely impacts upon the CIR, resulting in
a “sharp propagating discontinuity”: a plateau, and where there is a flattening of the
velocity gradient there is also an increase in density at similar velocities, but different
spatial locations.
The proposed physics behind the appearance of DACs – namely the collisional shock-
effect upon optical depths through development of a radial velocity plateau – can be
explained by the mechanisms behind the CIR model, and it is the co-rotating structure
which enables these variations in absorption to occur over far greater time-scales than that
attributed to the flow-time of the wind itself.
Sobolev with Exact Integration (SEI) code provides a measure of the Mqi product for a
given model, which for dominant ion species with qi ∼ 1, the results can therefore go toward
providing a measure of the mass-loss rate itself, M . However SEI code assumes a smooth
wind, and does not take into account any degree of clumpiness which may be present within
the outflow material, and which could have an affect upon the Mq values obtained via the
model. With this understanding one must therefore tale into consideration the ‘clumping’
filling factor of f∞ ∼0.08 implied in the results of the CMFGEN analysis as carried out
by Miguel Urbaneja (IoA, Hawai’i) and presented in Section 5 of this chapter; especially
considering the inherent sensitivity of the Pv resonance lines to clumping factors as well
as to mass-loss. Studies of O-type stars by Bouret et al. (2005) and Fullerton et al. (2006b)
have formulated a reduction factor by which mass-loss measured via smooth-wind studies
(such as SEI), should be reduced: by a factor of ∼ 1/√
f∞, i.e. for a clumping factor of
f∞ ∼ 0.08, the reduction factor for the mass-loss of NGC 6543 would be 1/√
0.08 ∼ 4. It
should also be noted that in optical studies of CSPNs, Kudritzki et al. (2006) undertook
analysis to establish the clump filling factors required to improve stellar emission fits of
Hα and He ii λ 4686, and it was shown that the adoption of filling factors improved fits of
their FASTWIND code.
However, Oskinova et al. (2007) argue that the introduction of clumping factors to
address the unreal homogeneity of stellar wind models (which are considered to cause
an over-estimation of mass-loss rates) has generalised the issue by an assumption of the
optical thinness of the clumps, with the result that the subsequent reduction of mass-loss
rate calculations by a factor of ∼3 actually results in an under -estimation of mass-loss
values. Their opinion is that the spatial separation of the clumps – the porosity of the
wind material – must be taken into account, and that modelling which incorporates larger
3.6. Conclusion 118
separations of optically-thick clumps is better able to fit the emission line profiles which
have now been detected in X-ray spectra of O stars.
Given the connection being established between wind models and mechanisms of O
stars and O-type CSPNs, this is yet another branch of spectroscopic research which can
help towards a further understanding and appreciation of the inherent astrophysics of
CSPNs.
Chapter 4
Structure in Fragmented
FUSE UV Time-Series Spectra
The structure observed in the wind of NGC 6543, as detailed in the previous chapter, gives
rise to speculation of NGC 6543 being unique among CSPNs, or whether it is possible to
see DAC-like forms in the winds of other CSPN objects; and to this end a selection of
objects was made with view to analyse further FUSE-based data. However the extent of
data in the archive is limited, and often disappointingly noisy or off-target. In this chapter
the focus will be upon four objects which, although posessing limited time-series data, can
still provide useful information upon general parameters for hydrogen-rich CSPNs.
From the STSci archive of data obtained via the FUSE satelitte it was necessary to seek
out data which fulfilled certain criteria necessary to undergo similar time-series analysis
as had been carried out on the UV data obtained for NGC 6543. Of primary importance
was that a given object must possess a number of sequential spectra, and not just one or
two. Also, the spectra must present clearly defined P Cygni profiles, the key signatures of
a expanding stellar atmosphere; what is more, the P Cygni profiles found within a given
object’s UV spectra need to be unsaturated in order to modelled as accutaely as possible
and obtain, via the SEI code, a measure of the mass-loss-ionisation-fraction product, Mq.
The data selected is listed below in Table 4.1.
119
120
Fig. 4.1. HST WFPC2 image of PN NGC 6826 (the ‘Blinking Nebula’), showingthe nebula’s gaseous composition with nitrogen (red), hydrogen (green), andoxygen (blue): http://apod.nasa.gov/apod/image/9712/
Fig. 4.2. Composite MMT near-infrared image of PN IC 2149, made up ofexposures taken via red (2.09 µm), green (2.19 µm), and blue (2.17 µm) filters:http://www.williams.edu/astronomy/research/PN/ nebulae/search/nebimages/
121
Fig. 4.3. HST WFPC2 image of PN IC 418 (the ‘Spirograph Nebula’), showingthe nebula’s gaseous composition with nitrogen (red), hydrogen (green), andoxygen (blue): http://www.astro.yale.edu/astro120/
Fig. 4.4. HST WFPC2 image of PN IC 4593, with filters depicting differ-ent nebula gases, namely nitrogen ([N ii] - red), helium (Hα - green), andoxygen ([O iii] - blue): http://hubblesite.org/gallery/album/entire/pr2007033d/largeweb/npp/all/
4.1. Fragmented Time-series Objects 122
Table 4.1. FUSE objects – details of observationsObject NGC 6826 IC 2149 IC 418 IC 4593
Dataset P1930401 P1041401 P1151111 B0320102
No. Exposures 12 8 9 4
UT Date 2000-08-07 1999-12-02 2001-12-02 2001-08-03
MJD (start) 51763.950 51514.132 52245.100 52124.645
∆T 1.6 6.1 1.2 0.5
4.1 Fragmented Time-series Objects
4.1.1 NGC 6826
A study of NGC 6826 (along with NGC 6543) (Perinotto et al. 1989) depitcs an early use
of the original SEI method (Lamers et al. 1987). Using the SEI method model fits were
obtained for the P Cygni profiles of C iv , N iv and Nv , O iv and O v . From the SEI
fits, the product of the mass-loss rate, M , and the averaged ionisation fraction qi, i.e. M qi,
is derived by intergrating between 0.2 and 0.8 of the normalised wind profile, w = v/v∞.
In order to obtain a value for the mass-loss rate itself, M , the ionisation hypothesis that
q(O iv ) + q(O v ) = 1 is used, from which NGC 6826 is assigned a mass-loss rate of M
= 5.2 ×10−8 M⊙ yr−1 (with 4.0 ×10−8 M⊙ yr−1 for NGC 6543). Once M is obtained then
the averaged ion fractions of the investigation ion profiles can be calculated.
4.1.2 IC 2149
IC 2149 possesses a perculiar morphology and is another of those PN which have benefitted
from the PN of the last twenty years or so whose investigations into various kinematic sce-
narios have provided possible means by which numerous PNs have evolved their elaborate
shapes (Sahai & Trauger 1998)
The prescence of a stellar wind is discerned from the appearance of P Cygni profiles
observed in the UV spectra (Perinotto et al. 1982), the terminal velocity of which is taken
from the edge of the saturated blue component of the C iv λ 1548.20, 1550.77 doublet.
Despite the indications of the manifestation of a stellar wind, as far as a possessing a
variable outflow, this latter phenomenon has not been observed (Patriarchi & Perinotto
1997).
4.1. Fragmented Time-series Objects 123
4.1.3 IC 418
Simultaneous spectroscopic and photometric exposures have been taken of the central star
of IC 418 with the aim of assessing the variability observed (Mendez et al. 1986), in an
atttempt to discern the cause whether due to hidden binarity or to (mono-)stellar pulsa-
tions; it had already been noted that the photometric velocity varied on a timesacle of
a few hours (Mendez et al. 1983). The variations were on too short a scale to indicate
being the result of a binary-system interaction; due to the compartively low-level fluc-
tuations of surface temperature, radial pulsations are not a likely cause; also non-radial
pulsations are not though of as a likely source of the variations as these do not appear to
be sinusoidal in nature, which would otherwise indicate the presence of waves traveliing
non-radially across the stellar surface. Therefore, the observed fluctuations are cause by
variations of the stellar outflow rate at the level of the photosphere, namely variations in
the optical thickness (depth) of the outflowing material, which because of the apparent
lack of temperature fluctuations, must be attributed to fluctuations in density, possibly
be caused by some unknown mechanism which switches on/off the mass at the bottom of
the expanding atmosphere, and with the continuing mass-loss above, there is a subsequent
drop in density, thus resulting in a drop in optical thickness.
The original format of the SEI method of modelling P Cygni profiles has been utilised
to model UV resonance lines from IUE data, and from these models the mass-loss rates,
M , can be estimated (Cerruti-Sola & Perinotto 1989): input parameters used are taken
from non-LTE hydrogen and helium model atmospheres giving temperature and gravities
for certain CSPNs. With both high- and low-resolution IUE data, Zanstra temperatures
were obtained, the theoretical stellar continuums have been compared to those observed
to gain futher temperature-based information, and the final temperatures have then been
used to estimate further stellar parameters.
An assumption utilised by Castor et al. (1981), that q(O iv ) + q(O v ) = 1, could
not be used as not both these ions were measurable for IC 418; however an alternative
assumption, gives that q(N iv ) + q(Nv ) = 1 also, and using the measured Mq for the
N iv and Nv ions, the mass-loss rate for IC 418 was estimated to be M = 6.3 × 10−9
M⊙ yr−1.
4.2. Time-Averaged Spectra & SEI Modelling 124
4.1.4 IC 4593
The fast winds of IC 4593 had also been investigated (Cerruti-Sola & Perinotto 1989) (CS)
using the (then) fairly recent wind analysis method, SEI (Lamers et al. 1987). Employing
a multi-parameter grid method, whereby varying input parameters were employed in the
construction of the SEI model, they (CS) were able to assess which combination produced
the best-fit model and therefore drew the conclusion that this was because the input
parameters were the optimum for that paticular object. The adoption of the grid method
was used instead of applying an input phospheric absoprtion line and not applying such
wind law parameters as termianl velocity, and a β acceleration parameter in order to
manipulate the photosperic absorption trough into shape-shifting into a P Cygni profile.
In estimating the mass-loss rate, M, from the SEI derived Mq, one, of couse, has to
have a value for the ionisation fraction, q of the ion modelleled. The assumption made by
Castor et al. (1981), that q(O iv ) + q(O v ) = 1, could not be used as IC 4593 does not
possess line profiles for both these ions in its spectra; however the second assumption that
q(N iv ) + q(Nv ) = 1, could be used as both these ions can be identified as lines in the
spectra, and so CS were able to predict a values for the mass-loss rate of the star, M =
4.2 ×10−8 M⊙ yr−1.
4.2 Time-Averaged Spectra & SEI Modelling
As with NGC 6543 in the previous chapter, the mean spectrum of each object was sub-
jected to SEI modelling, and again as with NGC 6543, the parameters of optical depth
and velocity FWHM have been estimated from rotationally-broadened spectral absorption
lines from photosperic spectra obtained via the TLUSTY Teff –log g grid of models. Each
P Cygni profile has been modelled with SEI and the resulting Mq values from the radial
optical depth fits have been recorded, as well as the average Mq value integrated between
the radial velocity bins 0.2 – 0.9 v∞.
The input parameters – see Table 4.2 – listed for NGC 6826, IC 418 and IC 4593
used for the SEI modelling procedure in this chapter, namely the individual objects’
wind’s terminal velocities, as well as their individual values for luminosity and effective
temperature (from which the respective stellar radii can be derived the code), have been
taken from the wind-analysis results of Kudritzki et al. (2006). The parameters list for IC
2149 have been taken from Perinotto et al. (1982). Although the terminal velocity for the
4.2. Time-Averaged Spectra & SEI Modelling 125
Table 4.2. FUSE objects – central star parametersObject NGC 6826 IC 2149 IC 418 IC 4593
v∞[km s−1] ±100 1200 1000 700 950∗
Teff[K] ±1000 46000 35000 36000 40000
log L/L⊙ ±0.01 4.11 3.24 4.38 4.05
Radius, R/R⊙ 1.8 2.0 4.0 2.2
Abundance, AE solar solar solar solar
Radial velocity [km s−1] −6.2 ±0.6 −30.7 ±2.1 +61.9 ±0.5 +22.0 ±0.5(Schneider et al. 1983)
stellar wind of IC 4593 is given by Kudritzki et al. (2006) as 900 km s−1, it was found that
in the SEI modelling of the blue component of Pv , the blue edge of the absorption trough
was better aligned with the underlying spectral absorption trough if the model’s terminal
velocity was adjusted up to 950 km s−1 *. The chemical abundances of the CSPNs have
been assumed to be solar.
4.2.1 Data Source & Ion Species – NGC 6826
The FUV spectra for NGC 6826 are taken from the P193 Program (PI – T.P. Snow),
obtained on 7th August 2000: 12 exposures were obtained over ∼1.6 hours (5796 s) via the
Lif2 Channel (segment A: 1087 – 1182 A) from which information on the Pv λλ 1117.98,
1128.01 doublet can be derived; likewise 12 exposures were obtained via the Lif2 Channel
(segment B: 979 – 1075 A) for the O vi λλ 1031.93, 1037.62 doublet.
In Figure 4.5 P Cygni profiles can be seen in the doublets of Pv and O vi ; also in
the non-resonance line of C iii λ 1175.66 there appears a P Cygni-like absorption trough -
emission peak pairing in its spectral profile.
4.2.2 SEI Model Fits – NGC 6826
P v λλ 1117.98, 1128.01
The SEI models for different ion species found in the outflow of NGC 6826 exhibit a wide
range of dgrees of development and saturation, see Figure 4.6. An SEI model fit has been
acheived for the unsaturated P v profile by applying a v∞ of −1200 km s−1 and β = 1.25
4.2. Time-Averaged Spectra & SEI Modelling 126
Fig. 4.5. Mean FUSE spectra for NGC 6826 highlighted with key resonancelines
upon a photospheric input Gaussian profile with a FWHM of ∼200 km s−1; however, the
absorption profile of Pv λ 1117.98 is relatively shallow and in exhibiting the geneneral
shape of a P Cygni profile with the extent of the depth of the absorption trough being
echoed in the height of the emission peak, this peak is similarly weak. In terms of the
radial optical depths the τrad(w) values range from 0.4 at w = 0.25 to 0.9 at w = 0.90. In
terms of the average Mq(P4+) , as integrated over 0.2 to 0.9 v∞, the SEI model predicts
a value of ∼ 6.8× 10−9 M⊙ yr−1, and over the limited data available the Mq(P4+) ranges
from a minimum of ∼ 5.3 × 10−9 M⊙ yr−1 and a maximum of ∼ 7.8 × 10−9 M⊙ yr−1.
O vi λλ 1031.93, 1037.62
In contrast the P Cygni profile for the O vi λ 1031.93 line has a much deeper absorption
trough and a subsequently stronger peak in emission: the SEI fits has been achieved with
a similar v∞ and β for a photospheric input Gaussian profile of FWHM ∼200 km s−1.
The P Cygni profile is highly saturated with the absorption trough reaching down to
zero flux; however it is not as saturated as to proceed to flatten out to the extent seen in
C iv λ 1548.20. Aside from the blending of the top of the blue edge of the absorption profile
4.2. Time-Averaged Spectra & SEI Modelling 127
Fig. 4.6. NGC 6826: SEI model fits for the mean spectra for the P v (l) andO vi (r) resonance lines shown above, with model fits for S vi (l) and C iii (r)shown below.
becoming blended with the adjacent absorption of Ly-β, thus preventing the blue O vi
component from merging back into the continuum, the SEI model is reasonable matched;
despite the saturation towards to blue edge of the absorption trough, the increased forward
scattering of the model does not move beyond the red edge of the absorption trough,
although it does appear to coincide. The optical depth histogram records a minumum
optical depth of 0.45 at w ∼ 0.2, increasing steadily to ∼ 3.5 up to w = 0.8 from where
the depth increses rapidly to a maxiumum of 7.4 at w = 0.9, after which it drops slightly
before the trough becomes blended with the Ly-β absoprtion. The red component of O vi
at λ 1037.62 possesses a better defined blue edge which is well matched by the model but
in the lower velocities (w ≤ 0.4), and beyond into emmission, the profile is affected by
interstellar ansorption, although at first glance the model appears to match the (albeit
4.2. Time-Averaged Spectra & SEI Modelling 128
estimated) shape of the P Cygni profile. The optical depth histogram shows a minimum
of 0.7 at w ∼ 0.2, increasing to 1.6 at w ≥ 0.9.
S vi λ 933.38
The blue component of the S vi λλ 933.38, 944.76 doublet is highly saturated, and although
possessing a clearly defined blue edge, the saturation in the absorption has forced the model
to produce excessive forward scattering which extend to the blue edge of the trough: the
subsequent optical depth histogram is unlikely to reflect the true nature of the absorption
in terms of the τrad values it displays which can only be taken as the lower limit of the
radial optical depths.
4.2. Time-Averaged Spectra & SEI Modelling 129
4.2.3 Data Source & Ion Species – IC 2149
The FUV spectra for IC 2149 are taken from the P104 Program (PI – Warren Moos),
obtained on 2nd December 1999: 8 exposures were obtained over ∼6.1 hours (21910 s)
via the Lif2 Channel (segment A: 1087 – 1182 A) for the P v λλ 1117.98, 1128.01 dou-
blet; 8 exposures were obtained via the Lif2 Channel (segment B: 979 – 1075 A) for the
O vi λλ 1031.93, 1037.62 doublet; and 8 exposures also obtained via the Sic2 Channel
(segment A: 917 – 1006 A) for the S vi λλ 933.38, 944.52 doublet.
Under the P104 Program 9 exposures were also obtained over ∼4.5 hours (16228 s)
on 25th November 1999, and a further 12 exposures over ∼4.8 hours (17171 s) on 14th
January 2000; however, when this data was applied to the TVS algorithm, the power
output showed limited variance above the 95% confidence level – Figure 4.21 below – and
so was not investigated further.
In Figure 4.7, as well as P v and O vi a vague P Cygni appears at S vi λ 933.38 but not
at S vi λ 944.52, as well as a contaminated P Cygni at C iii λ 977.03; although it does show
a blueward absorption. C iii λ 1175.66 has a slight redward emission peak but is rather
shallow and therefore not a strong P Cygni profile, but again there is a strong blueward
(unsaturated) absorption trough.
4.2.4 SEI Model Fits – IC 2149
P v λλ 1117.98, 1128.01
As seen in Figure 4.8, the SEI model of the P v profile of IC 2149 – modelled using v∞ =
−1000 km s−1 and β = 1.25 upon an input Gaussian of FWHM ∼ 200 km s−1 – is similar to
that of NGC 6826 in that the profile is unsaturated to the extent of appearing a weak line
- but in contrast to NGC 6826 the adopted optical depth profile τ(w) peaks at 0.9 at a the
lower (normalised) velocity of w = 0.25, with the profile becoming shallower towards the
wind terminal velocity, dropping to a low τ(w) of 0.05 at w = 0.93. The average Mq(P4+) ,
(integrated, as before, over 0.2 to 0.9 v∞), gives a value of ∼ 1.5 × 10−9 M⊙ yr−1, and
over the limited data available the Mq(P4+) ranges (to a much lesser extent than seen in
NGC 6826) from a minimum of ∼ 1.3 × 10−9 M⊙ yr−1 and a maximum of ∼ 1.7 × 10−9
M⊙ yr−1.
4.2. Time-Averaged Spectra & SEI Modelling 130
Fig. 4.7. Mean FUSE spectra for IC 2149 highlighted with key resonance lines
O vi λλ 1031.93, 1037.62
The blue component of the O vi λλ 1031.93, 1037.62 doublet is blended with the red edge
of the Ly-β interstellar line and so aligning the blue edge of the O vi model – upon
an input Gaussian profile of FWHM ∼ 300 km s−1 – is at best a rather rough estimate;
otherwise the remainder of the absorption trough is well matched. Although strong in
absorption the trough does not appear saturated and there is no excessive scattering to
affect the model, therefore the profile is well matched as far back as the emission peak
which although affected by interstellar absorption is also well matched by the model. The
τrad histogram shows that the optical depth is lowest at low velocity with τ(∼ 0.2) = 0.5,
rising to τ(0.85) = 2.4; blue edge values of optical depth are unreliable however, because of
the interstellar absorption from w > 0.8. The red O vi component is excessively affected
by interstellar absorption and so, unlike with NGC 6826, no attempt has been made to
model its profile.
4.2. Time-Averaged Spectra & SEI Modelling 131
Fig. 4.8. IC 2149: SEI model fits for the mean spectra for the P v (l) andO vi (r) resonance lines.
4.2. Time-Averaged Spectra & SEI Modelling 132
4.2.5 Data source & Ion Species – IC 418
The FUV spectra for IC 418 are taken from the P115 Program (PI – Michael Shull),
obtained on 2nd December 2001: 9 exposures were obtained over ∼1.2 hours (4423 s) via
the Lif2 Channel (segment A: 1087 – 1182 A) for the P v λλ 1117.98, 1128.01 doublet can
be derived; 9 exposures were obtained via the Lif1 Channel (segment A: 987 – 1082 A) for
the O vi λλ 1031.93, 1037.62 doublet; and 9 exposures also obtained via the Sic2 Channel
(segment A: 917 – 1006 A) for the S vi λλ 933.38, 944.52 doublet.
P Cygni profiles can be seen in Figure 4.9 for Pv λλ 1117.98, 1128.01 and O vi λλ 1031.97,
1037.62 but not for S vi λλ 933.38, 944.52 simply saturated absorption. P Cygni profiles
can also be seen at C iii λ 977.03 (saturated), S iv λ 1072.97 (unsaturated), and also at
C iii λ 1175.66 (strong absorption but not quite saturated).
There is also strong blueward absorption at N iv λ 955.34 and S iv λ 1062.66 but not
the full absorption-emission P Cygni profile.
Fig. 4.9. Mean FUSE spectra for IC 418 highlighted with key resonance lines
4.2. Time-Averaged Spectra & SEI Modelling 133
Fig. 4.10. IC 418: SEI model fits for the mean spectra for the P v (l) andO vi (r) resonance lines shown above, with model fits for S vi (l) and C iii (r)shown below.
4.2.6 SEI Model Fits – IC 418
P v λλ 1117.98, 1128.01
The SEI model of the P v profile of IC 418 is modelled using v∞ = −700 km s−1, but now
the P v profile is fitted with a faster acceleration profile for β = 0.85 (upon an photospheric
input Gaussian of FWHM ∼ 200 km s−1). As seen in Figure 4.10, IC 418 possesses a much
stronger P Cgyni profile to either that of NGC 6826 or IC 2149 but still unsaturated. The
optical depth profile τ(w) peaks at 0.9 at a the lower (normalised) velocity of w = 0.25,
with the profile becoming shallower towards the wind terminal velocity, dropping to a low
τ(w) of 0.05 at w = 0.93. The average Mq(P4+) , (over 0.2 to 0.9 v∞), gives a value
of ∼ 1.2 × 10−8 M⊙ yr−1, and over the limited data available the Mq(P4+) ranges (to a
much lesser extent than seen in NGC 6826) from a minimum of ∼ 1.3×10−9 M⊙ yr−1 and
4.2. Time-Averaged Spectra & SEI Modelling 134
a maximum of ∼ 2.4 × 10−9 M⊙ yr−1.
O vi λ 1031.93
An attempt has been made to model the blue component of the O vi λλ 1031.93, 1037.62
doublet (v∞ = −700 km s−1, β = 0.85, photospheric input Gaussian of FWHM ∼ 350
km s−1); however the blue edge of the absorption trough (and also the continuum further
bluewards) has been too much affected by interstellar line absorption to achieve a confi-
dently modelled profile, indeed even a high dispersion parameter of vturb = 0.30 cannot
match the blue edge which has been all but removed by the interstellar lines. The corre-
sponding histogram shows a low value of τ(w) in the velocity range 0.00 ≤ w < 0.50, from
where the rest of the histogram shows a steady increase from τ(0.55) = 0.5 to τ(1.00) =
4.2. The red component is much worse affected by interstellar absorption and subsequently
any P Cygni profile that might otherwise exist has been hidden.
S iv λ 1072.97
In contrast, the red component of the S iv λλ 1062.66, 1072.97 doublet is minimally affected
by interstellar line absorption and so the P Cygni profile has been well matched with similar
wind law parameters (v∞, β) as P v above (photospheric input Gaussian: FWHM ∼ 300
km s−1), requiring only a slight increase in the wind dispersion of vturb = 0.12 to match the
blue wall of the model with that of the absorption trough underneath. The corresponding
τrad histogram shows a steady increeas in optical depth from 1.8 at ∼ τ(0.2) to a maximum
τ(0.7) = 3.2 before decreasing again to 0.8 in the velocity range of the blue edge, 0.90
≤ w < 1.00.
Si iv λ 1393.76
In addition, the blue component of the Si iv λλ 1393.76, 1402.77 has been modelled, the
spectrum obtained via the IUE archive (SWP 37763). Again with similar velocity param-
eters (v∞, β, photospheric input Gaussian: FWHM ∼ 350 km s−1) the profile has been
well matched by the model; however a slightly higher v∞ of 750 km s−1 had to be adopted
in order to align the blue edge of the SEI model absorption component with that of the
observed line profile, with only a slight increase of velocity dispersion to vturb = 0.10. The
τrad histogram shows that from 2.0 at ∼ τ(0.2) the optical depth increases to a maximum
4.2. Time-Averaged Spectra & SEI Modelling 135
of 4.2 between 0.60 ≤ w ≤ 0.70 before decreasing again to 2.4 at the blue edge, 0.90 ≤ w <
1.00.
4.2.7 Data Source & Ion Species – IC 4593
The FUV spectra for IC 4593 are taken from the B032 Program (PI – Robert Gruendl),
obtained on 3rd August 2001: only 4 exposures were obtained over ∼0.5 hours (1933 s)
via the Lif2 Channel (segment A: 1087 – 1182 A) for the P v λλ 1117.98, 1128.01 doublet
can be derived; 3 exposures were obtained via the Lif1 Channel (segment A: 987 – 1082
A) for the O vi λλ 1031.93, 1037.62 doublet; and 3 exposures also obtained via the Sic2
Channel (segment A: 917 – 1006 A) for the S vi λλ 933.38, 944.52 doublet.
P Cygni profiles can be seen for P v λλ 1117.98, 1128.01 and O vi λλ 1031.97, 1037.62
and very subtley for S vi λλ 933.38, 944.52 the second line of which shows only the smallest
redward emission peak. P Cygni profiles can also be seen at C iii λ 977.03 (saturated) and
C iii λ 1175.66 (strong but unsaturated).
Strong blueward absorption can also be seen at N iv λ 955.34 and although there may
be blueward absorption at S iv λ 1072.97 but it is weak and indistinct.
Fig. 4.11. Mean FUSE spectra for IC 4593 highlighted with key resonance lines
4.2. Time-Averaged Spectra & SEI Modelling 136
4.2.8 SEI Model Fits – IC 4593
Fig. 4.12. IC 4593: SEI model fits for the mean spectra for the P v (l) andO vi (r) resonance lines shown above, with model fits for S vi (l) and C iii (r)shown below.
P v λλ 1117.98, 1128.01
An SEI model of the P v profile of IC 4593 was initially attempted using v∞ = −900
km s−1(Kudritzki et al. 2006), however a much better fit, with the blue edge of the model
aligning itself closer with that of the underlying spectra, was acheived with v∞ = −950
km s−1 (which is 50 km s−1 higher but within the ± 100 km s−1 error limit of Kudritzki),
upon a photospheric input Gaussian of FWHM ∼ 250 km s−1. Also the β factor of the
wind’s acceleration profile possesses has been increased from 1.25 of NGC 6826 and IC
2149 (and NGC 6543 in chapter 3) to a factor of β = 1.50. IC 4593 has a much stronger
P Cgyni profile to either that of NGC 6826 or IC 2149 but still unsaturated. The optical
4.2. Time-Averaged Spectra & SEI Modelling 137
depth profile τ(w) peaks at 0.9 at a the lower (normalised) velocity of w = 0.25, with the
profile becoming shallower towards the wind terminal velocity, dropping to a low τ(w) of
0.05 at w = 0.93. The average Mq(P4+) , (over 0.2 to 0.9 v∞), gives a value of ∼ 1.2×10−8
M⊙ yr−1, and over the limited data available the Mq(P4+) ranges (to a much lesser extent
than seen in NGC 6826) from a minimum of ∼ 1.3 × 10−9 M⊙ yr−1 and a maximum of
∼ 2.4 × 10−9 M⊙ yr−1.
O vi λλ 1031.93, 1037.62
The P Cygni profile at O vi λ 1031.93 has also beem modelled with v∞= −950 km s−1and β
= 1.50 (photospheric input Gaussian: FWHM ∼ 250 km s−1), but an increased dispersion
parameter of 0.30 in order to better fit the blue edge of the model; unfortuately as high
vturb parameters have a tendency to smooth out the model profile this has had the effect
of lowering the emission peak in the model and so this aspect of the P Cygni is matched
less satisfactorily. The edge of the blue component of the O vi doublet is also affected by
interstellar line absorption (particularly the adjacent Ly-β) which has effectively removed
the contiuum bluewards of O vi and so modelling the blue component is often difficult;
however a SEI fit of the red component, O vi λ 1037.62 has been acheived, again with v∞
= −950 km s−1 and β = 1.50 (photospheric input Gaussian of ∼ 200 km s−1), but a lesser
dispersion parameter of vturb = 0.10, and despite significant interstellar line interference
the underlying emission peak is better matched by the model.
Si iv λ 1393.76
An additional P Cygni profile is found in an IUE spectrum (SWP 17948) for the blue
component of the Si iv λλ 1393.76, 1402.77 doublet: this is well match by the parameters
of v∞ = −950 km s−1, β = 1.50 (photospheric input Gaussian: FWHM ∼ 350 km s−1) and
a low dispersion vturb = 0.05. Despite minimal interstellar lines and the model predicting
slightly excessive forward scattered emission between 0 and 0.2 v∞, the model is fitted
satisfactorily in the velocity range 0.25 ≤ w < 1.00. The τradhistogram seems to comprised
of two components in that τ(w) steadily decreases from 1.3 at w = 0.3 to 0.4 at w = 0.65,
before rapidly increasing to 1.5 at w = 0.8, and again falling to 0.2 at w = 0.93. Of these
two ‘components’, the former is interesting as it resembles (perhaps only superficially)
the pattern of the τrad fitting seen in that of the blue Pv component in the sequential
time-series spectra of NGC 6543 in chapter 3, where such a relatively deep absorption
4.3. Time Variability Characteristics 138
Table 4.3. FUSE objects average mass-loss-ionisation fractions [M⊙ yr−1]
Object P v 1118 O vi 1032 O vi 1037 S vi 933 S iv 1073 Si iv 1394
NGC 6826 6.8 e-09 6.7 e-11 4.2 e-11 8.1 e-10 – –IC 2149 1.5 e-09 1.4 e-11 – – – –IC 418 1.2 e-08 1.5 e-11 – – 2.4 e-09 1.8 e-10IC 4593 9.3 e-09 3.1 e-11 4.3 e-11 – – 2.1 e-11
in the lower velocity part of the absorption profile could be attributable to a DAC-like
feature, especially at the feature was seen to migrate bluewards before fading into the
deeper absorption closer to the blue edge of the trough; unfortunately the IUE archive
does not possess such time-series spectra as might be able to display such a DAC-like
migration, and so this must remain speculation.
All average Mq values across all modelled P Cygni profiles are listed in Table 4.3, and
as with the Mq calculations via SEI code for NGC 6543 as detailed in Chapter 3, the
estimated error in of the order of ∼ 20%.
4.3 Time Variability Characteristics
The information as regards variability which can be obtained from such in-extensive data
is limited. Although one can attempt TVS analyses upon the time series data for each
object, due to the limited exposures available, the resulting TVS spectra may not reflect
the true extent of the variability. Indeed for IC 4593 there are only four FUSE exposures
available and so TVS analysis of such a limited sample is inconclusive. As regards further
Fourier-based analyses upon the data, again the limited number of exposures over narrow
timescales is far too sparse to be able to produce any Fourier power spectra of any value
regarding the revelation of modulation periods. Instead, until such extensive data becomes
avaliable, the initial TVS analysis will at least provide information as the to velocity range
across which any variability becomes apparent; the corresponding greyscale plots may, as
in the previous chapter, reveal the presence of large scale structures within the wind, which
migrate bluewards through the wind over time.
4.3. Time Variability Characteristics 139
Fig. 4.13. NGC 6826: Overplot of P v doublet spectra illustrating the variablenature of the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 on theright.
4.3.1 Time Variability – NGC 6826
The overplot of spectra depicting minimum and maximum absorption – Figure 4.14 –
shows a significant variation in the absorption trough of Pv λ 1117.98, as well as a narrow
variable margin in the emission peak; also in the absorption trough of P v λ 1128.01 but
across a narrower velocity range than its more blueward counterpart.
4.3. Time Variability Characteristics 140
Fig. 4.14. NGC 6826: Dual spectra plot depicting Pv doublet with minimum(black) and maximum (red) absorption.
4.3. Time Variability Characteristics 141
2.0
4.0
6.0
8.0
10.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Flu
x
5.0
10.0
15.0
20.0
25.0
30.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0 1000 2000Velocity (km/s)
0.5
1.0
1.5
Flu
x
Fig. 4.15. TVS analysis plots (below) of the P Cygni profiles of theP v λλ 1117.98, 1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of NGC6826, where the upper panel of each TVS profile depicts the variance statistic,with changes above the 95% significance level (dotted line) highlighted. Thecorresponding greyscale depiction of each line profile’s time-series spectra is alsoshown (above) depicting the temporal changes in the (vertically stacked) indi-vidual spectra, all normalised by the corresponding mean profile as shown in thelower panel beneath the TVS significance profile; the dynamical range of thegreyscales on this page – and all subsequent greyscales in this chapter – is 0.95(black) to 1.05 (white).
4.3. Time Variability Characteristics 142
The TVS displays in Figure 4.15 show variation in the absorption of the P v λλ 1117.98,
1128.01 doublet, which for the blue component extends over an approximate range of −750
– 0 km s−1; for the red componet the TVS shows significant variability between −1000 –
+250 km s−1; the TVS also indicates a narrow spike in the region of the blue component
emission peak, across an approximate (maxiumum) range of between 0 – +100km s−1. Not
so in the TVS display for the O vi λ 1031.93, 1037.62 doublet, only in the emission peaks
which unfortunately tends to mask any possible blue-edge variation of the O vi λ 1031.93
saturated absorption trough.
The equivalent width of the absorption trough in the blue component, as measured
between 1112.8 and 1118.2 A, is also variable between exposures, varying between a min-
imum of 0.8 A to a maximum of 1.3 A, with a mean of 1.1 A (s.d: 0.2 A); the emission
peak, as measured between 1118.0 and 1120.9 A, varies between 0.5 and 0.7 A, with a
mean of 0.6 A (s.d: 0.1 A).
Figure 4.15 illustrates the problem with greyscale images based upon a limited number
of exposures: as the few spectra available are stitched together by the greyscale imaging
algorithm, the result is a smearing effect as the time-axis limits of each exposure are merged
to produce a continous display across the entire duration of the observation (i.e. the scale
of the y-axis). It is therefore difficult pinpoint with a cursor precise loci of apparently
migrating DAC-like features in terms of changing velocity and the corresponding time-
reference. One solution is to reduce the resolution level of the time-axis from the greyscale
(from the default setting of 500 to the low level of 10): this has the effect, as seen in
Figure 4.16 of producing a stacked series of low resolution spectral strips which therefore
allow for slightly more accurate estmations of the DAC’s progressions in velocity and time
which otherwise would not be possible; it also provide a clearer means by which one can
estimate the errors of v and t.
Thus using such low-resolution greyscale images a series of esimated velocity-time
coordinates can be obtained and consequently an estimate of the average accelerations of
select DAC-like features can be derived from a least-squares method. The velocities of
two such features have in the low-res. greyscale of the blue component of the P v doublet
have been estmated – see Table 4.4 – and the resulting velocity-time coordinates have
been plotted and superimposed by the subsequent least-squares average acceleration, as
shown in Figure 4.17: both DAC-like features have an estimated average acceleration of
∼ 2 × 10−2 km s−2 (with an estimated error of around 10%).
4.3. Time Variability Characteristics 143
Fig. 4.16. Low-resolution greyscale of P v doublet from which approximatemesurements can be taken of both velocity and time index of the bluewardprogression of the DAC-like features observed in the greyscale display of theP1930401 data of PN NGC 6826 in order to estimate the albeit (linear and there-fore approximate) acceleration of the ‘DACs’.
Unfortunately this P1930 observation was unable to produce any clearly-defined spec-
tra in either the 2asic or the 1bsic ranges i.e. for the ∼ 900 - 1000 A wavelength range;
however, an alternative dataset, that of the F160 Program, does exhibit clear spectra in
this range as well, but unfortunately it shows little variability – for S vi λλ 933.38, 944.52,
N iv λ 955.34, C iii λ 977.02 – when investigated for time-variance.
4.3.2 Time Variability – IC 2149
Earlier studies of IUE UV data, have reported that no variability in the apparent stellar
wind can be detected (Patriarchi & Perinotto 1997), so it is with a sense of intrigue that
one applies the temporal-variability analysis techniques to the FUV data from FUSE,
which provides spectral data over three nights.
As can be seen below in the TVS outputs of Figure 4.21, from P1041402 (1st obser-
vation: UT date 1999-11-25) and P1041403 (3rd observation: UT date 2000-01-14), the
TVS doesn’t show any significant varaiability across the Pv doublet, only the narrow-
4.3. Time Variability Characteristics 144
Table 4.4. NGC 6826 P v DAC progressBlueward Velocity Time
km s−1 [MJD 51764 +]
892 0.03962 0.061055 0.101126 0.131137 0.16
564 0.13670 0.16775 0.19845 0.22857 0.25903 0.28
est peaks which could simply reflect the random variability in noise levels. However, for
the P1041401 data (2nd observation: UT date 1999-12-02), a greater spread of variability
across the doublet is indicated, see Figure 4.20: between approximately −100 – −500
km s−1 in the blueward component (λ0 = 1117.98 A), and (approximately) across a range
between −400 – 0 km s−1 with regard to the red component (λ0 = 1128.01 A).
The equivalent width of the absorption trough of the blue component of P v , as
measured between 1113.6 and 1118.1 A, varies between 0.8 and 0.9 A (mean 0.9 A, s.d.
0.1 A); the emission peak, as measured between 1117.9 and 1121.5 A, varies between 0.3
and 0.5 A (mean 0.4 A, s.d. 0.1 A).
As with NGC 6826, the TVS for the P v doublet of IC 2149 – Figure 4.20 – shows a
tendency for variability in the absorption troughs: between −1000 – 0 km s−1 in the blue
component, and between −400 – 0 km s−1 in the red component. For the O vi doublet
however the TVS is dominated by the strong variance peak for the Ly-β emission peak,
but even with this dominating the TVS output, some variability in the O vi doublet
could exist in the absorption trough of Ovi λ 1031.93 and perhaps in the blue-edge of
O vi λ 1037.62.
In the image of the minimum absorption (maximum flux) overplotted with the spec-
trum of maximum absorption (minimum flux) – Figure 4.19 – there is only an obvious
difference between the two spectra across the lower velocities of the P v λ 1117.98 resonance
line; the other seems to possess little difference between the two extreme cases.
4.3. Time Variability Characteristics 145
Fig. 4.17. The two sets of velocity-time coordinates of the DAC-like featureobserved in the low-resoultion greyscale of the NGC 6826 P1930401 UV data areplotted and a least-squares algorithm has calculated the gradient of the best-fitline through the points: the acceleration of the first DAC-like feature is approx-imated at ∼ 2.4 × 10−2 km s−2; the acceleration of the second is similarly fittedand approximated at ∼ 2.5 × 10−2 km s−2.
As in the initial greyscale image of the P v doublet of NGC 6826, the lack of exposures
for the IC 2149 data of P1041401 is also blended in an attempt to display the changing
spectral profile across the duration of the night’s observation. As well as with NGC 6826
the time resolution of the greyscale has been reduced (again to the low level of 10) with
the result of a stacked series of spectra from which one can estimate the velocity-time
loci of a blueward-progressing DAC-like feature seen in the absorption trough of the blue
component of the P v doublet – see Table 4.5.
Again, as with the DAC-like features in NGC 6826, the velocity-time estimates for the
DAC in the P v doublet can be applied to a least-squares algorithm and a subsequent
average acceleration can be derived: this is shown in Figure 4.23 where the acceleration is
estimated as ∼ 2 × 10−2 km s−2 (again with an error of around 10%).
4.3. Time Variability Characteristics 146
Fig. 4.18. IC 2149: Overplot of P v doublet spectra illustrating the variablenature of the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 on theright.
Fig. 4.19. IC 2149: Dual spectra plot depicting P v doublet with minimum(black) and maximum (red) absorption.
Table 4.5. IC 2149 P v DAC progressBlueward Velocity Time
km s−1 [MJD 51514 +]
190 0.05213 0.09319 0.13389 0.17436 0.21588 0.25646 0.29716 0.34740 0.38
4.3. Time Variability Characteristics 147
2.0
4.0
6.0
8.0
10.0
12.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.2
0.4
0.6
0.8
1.0
1.2
Flu
x
20.0
40.0
60.0
80.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0 1000 2000Velocity (km/s)
0.0
0.5
1.0
1.5
Flu
x
Fig. 4.20. TVS analysis plots (below) of the P Cygni profiles of theP v λλ 1117.98, 1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC2149; the corresponding greyscale depiction of each lines time-series spectra isalso shown (above).
4.3. Time Variability Characteristics 148
2.0
4.0
6.0
8.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.2
0.4
0.6
0.8
1.0
1.2
Flu
x
4.0
6.0
8.0
10.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.2
0.4
0.6
0.8
1.0
1.2
Flu
x
Fig. 4.21. IC 2149: TVS & greyscale outputs for the P v doublet of the 1st (l)and 3rd (r) nights’ data.
4.3. Time Variability Characteristics 149
Fig. 4.22. A low-resolution greyscale of P v doublet from which an approximatemeasurement can be taken of both velocity and time index of the blueward pro-gression of the DAC-like feature observed in the greyscale display of the P1041401data of PN IC 2149 in order to estimate the albeit (linear and therefore approx-imate) acceleration of the ‘DAC’.
4.3. Time Variability Characteristics 150
Fig. 4.23. The velocity-time index coordinates as measured from the low-resolution greyscale of the IC 2149 P1041401 UV data are plotted and a least-squares algorithm has calculated the gradient of a best line fit through the points:the linear (and therefore approximate) acceleration of the DAC-like feature istherefore estimated at ∼ 2.1 × 10−2 km s−2.
4.3. Time Variability Characteristics 151
4.3.3 Time Variability – IC 418
Fig. 4.24. IC 418: Overplot of P v doublet spectra illustrating the variablenature of the resonance profile: P v λ 1117.98 on the left and P v λ 1128.01 onthe right.
The overplot of minimum (black) and maximum (red) absorption in the P v doublet –
Figure 4.25 – taken from the 2alif spectra, shows the extremes of the flux levels but does
not satisfactorily reproduce the relative low level of variance as picked up by the TVS.
Fig. 4.25. IC 418: Dual spectra plot depicting P v doublet with minimum(black) and maximum (red) absorption.
The TVS outputs for IC 418 in Figure 4.26 show a little variability in the P v doublet:
a narrow margin in absorption, between −50 – −25 km s−1, and between 0 – +25 km s−1
in emission for the blue component (λ0 = 1117.98 A); the red component (λ0 = 1128.01
4.3. Time Variability Characteristics 152
A) shows variation over a narrow −300 – −200 km s−1 margin in the absorption trough,
and three significance peaks across approximately 0 – +300 km s−1 in the (relatively low)
emission peak. There is no real indication of any variation in the saturated O vi doublet
(only a strong TVS peak in the region of the Ly-β emission spike).
In terms of equivalent width, the blue Pv component absorption trough, as measured
between 1113.8 and 1118.5 A, varies between 1.2 and 1.4 A (mean 1.3 A, s.d. 0.1 A); the
EW of the emission peak, measured between 1118.3 and 1121.1 A, varies between 0.2 and
0.5 A (mean 0.3 A, s.d. 0.1 A).
4.3. Time Variability Characteristics 153
2.0
4.0
6.0
8.0
10.0
12.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.20.40.60.81.01.21.4
Flu
x
5.0
10.0
15.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0 1000 2000Velocity (km/s)
0.20.40.60.81.01.2
Flu
x
Fig. 4.26. TVS analysis plots (below) of the P Cygni profiles of theP v λλ 1117.98, 1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC418; the corresponding greyscale depiction of each lines time-series spectra is alsoshown (above).
4.3. Time Variability Characteristics 154
2.0
4.0
6.0
8.0
10.0
12.0
14.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0Velocity (km/s)
0.20.40.60.81.01.21.4
Flu
x
Fig. 4.27. IC 418: TVS & greyscale outputs, centred on the stronger red com-ponent of the S iv λλ 1062.66, 1072.97 doublet.
4.3. Time Variability Characteristics 155
4.3.4 Time Variability – IC 4593
Fig. 4.28. IC 4593: Overplot of P v doublet spectra illustrating the variablenature of the resonance profile: P v λ 1117.98
Fig. 4.29. IC 4593: Dual spectra plot depicting P v doublet with minimum(black) and maximum (red) absorption.
For the central star of IC 4593, in terms of the FUSE data, there is an extremely limited
number of exposures: only four from B0320102. With so few spectra it is impossible to
detect any indication of any variability in the limited data; indeed, even in the image of
the over plotted spectra – Figure 4.29 – it is difficult to determine whether the fluctuations
are true variability or simply noise. The TVS outputs of Figure 4.30 for both the P v and
the O vi doublets fail to show any significant variance.
4.3. Time Variability Characteristics 156
10.0
20.0
30.0
40.0
(TV
S)1/
2 (%
FC)
−2000 −1000 0 1000 2000 3000Velocity (km/s)
0.20.40.60.81.01.21.41.6
Flu
x
2.0
4.0
6.0
8.0
10.0
12.0
14.0
(TV
S)1/
2 (%
FC)
−3000 −2000 −1000 0 1000 2000Velocity (km/s)
0.5
1.0
1.5
Flu
x
Fig. 4.30. TVS analysis plots (below) of the P Cygni profiles of theP v λλ 1117.98, 1128.01 (l) and O vi λλ 1031.93, 1037.62 (r) UV doublets of IC4593; the corresponding greyscale depiction of each lines time-series spectra isalso shown (above).
4.3. Time Variability Characteristics 157
2.0
4.0
6.0
8.0
10.0
12.0
14.0
(TV
S)1/
2 (%
FC)
−1000 0 1000 2000 3000Velocity (km/s)
0.2
0.4
0.6
0.8
1.0
1.2
Flu
x
Fig. 4.31. IC 4593: TVS & greyscale outputs for the S iv λλ 1062.66, 1072.97doublet.
4.4. Summary 158
4.4 Summary
The main aim of this chapter has been to try to replicate some of the results of the analysis
of NGC 6543 in the previous chapter: to examine whether the structure found within the
outflow of NGC 6543 – particularly the DAC-like feature seen migrating bluewards within
the absorption troughs of the Pv λλ 1117.98, 1128.01 doublet – could be observed in the
outflows of other CSPNs. The unfortunately-limited FUSE UV spectra of four other
CSPNs has been subjected to similar time-variance analysis techniques: the TVS analysis
had been applied to the time-series spectra available and subsequent greyscale displays
have provided image-based representations of any variabilty contained therein. As well,
SEI modelling has been applied to certain P Cygni profiles contained in the UV spectra
and measures of Mq have been obtained. The variablilty exhibited in the shapes of the P
Cgyni profiles, particularly the blue component of the Pv doublet, of these four CSPNs, is
reflected in the fluctuations in the measured value of the blue P v components’ equivalent
widths, details of which are collated in Table 4.6.
Table 4.6. FUSE objects’ P v equivalent width measurements [A]
Object Wavelength Range [A] Min EW – Max EW Mean EW SD
NGC 6826 1112.8 – 1121.4 0.31 – 0.92 0.62 0.20IC 2149 1113.5 – 1121.5 0.35 – 0.67 0.47 0.10IC 418 1113.6 – 1120.0 0.83 – 1.12 0.98 0.11IC 4593 1113.4 – 1121.7 0.53 – 0.73 0.63 0.08
The TVS analysis of the FUSE spectral sections containing the unsaturated P v dou-
blet have shown the greatest variability across a wider velocity range than other P Cygni
profiles such as the more saturated O vi λλ 1031.93, 1037.62 doublet; the extent of the
P v doublet variability, as measured in terms of the central velocity of each component,
is detailed below in Table 4.7 for each of the four fragmented time-series targets.
Table 4.7. FUSE objects’ P v TVS (approximate) variability ranges [km s−1]Object Variance Detected Blue Component Red Component
λ0 = 1117.98 A λ0 = 1128.01 A
NGC 6826 yes −750 – 0 −1000 – +250IC 2149 yes −1000 – 0 −400 – 0IC 418 yes −50 – −25 & 0 – +25 −300 – −200 & 0 – +300IC 4593 no – –
4.4. Summary 159
The P1930401 data of NGC 6826 and the P1041401 data of IC 2149 have demonstrated
higher levels of variability, and this can be seen in the resulting greyscales which appear
to show DAC-like features which migrate towards the blue edge of the absorption troughs
of their respective P Cygni profiles: from the NGC 6826 P1930401 data, the two DACs
migrate between ∼ −900 and ∼ −1150 km s−1 and between ∼ −550 and ∼ −900 km s−1;
the DAC seen in the IC 2149 P1041401 data appears to migrate between ∼ −200 and
∼ −750 km s−1 (see Table 4.8 below). The limited number, and non-uniform time index
spacing of the exposures in such data proves a handicap when trying to observe the
blueward migration of these DAC-like features: only a reduced resolution of the time-axis
can help towards a rough estimate of the average acceleration of the DAC-like features.
For the two DACs seen within the NGC 6826 data, and also the DAC observerd in the
IC 2149 data, the average acceleration is ∼ 2× 10−2 km s−2, which when re-scaled by the
R⋆/v∞ flow-time factor of each object respectively, gives a (dv/dt)(R⋆/v∞) of ∼ 25 km s−1
for NGC 6826 and ∼ 29 km s−1 for IC 2149 – both of which compare favourably with
the upper (dv/dt)(R⋆/v∞) factor for NGC 6543 of ∼ 26 km s−1, as shown in the previous
chapter – and all three are of a similar order to that given for the O7 III star example
mentioned in Chapter 3, namely ∼ 10 km s−1.
Table 4.8. FUSE objects’ P v DAC migrationDAC Velocity Range [km s−1] ∆T Acceleration [km s−2] ×R⋆/v∞NGC 6826 A −900 – −1150 ∼0.13 d 2.4 ×10−2 ∼25 km s−1
NGC 6826 B −550 – −900 ∼0.15 d 2.5 ×10−2 ∼25 km s−1
IC 2149 −200 – −750 ∼0.33 d 2.1 ×10−2 ∼29 km s−1
The lack of extensive datasets for these CSPNs – in terms of a large number of expo-
sures – prevents one from subjecting such time-series data to a proper Fourier analysis in
order to try and uncover any potentially periodic modulation of such structures. However
this chapter has shown that the existence of DAC-like features, as seen within the spectra
of NGC 6543 in the previous chapter, is not an isolated phenomenon; but whether this
is a common feature of CSPN outflows or not, can only be properly investigated with a
sufficiently extensive wealth of time-series data.
However, it should be pointed out that despite the lack of time series data available for
CSPNs, this study has managed to present evidence of DAC-like stuctures in the outflows
of three (possibly four) central stars; and therefore this might suggest that structured
4.4. Summary 160
winds may be as prevalent in CSPN outflows as they appear to be in the UV spectra of
the stellar winds of O stars.
Chapter 5
ESO Optical Spectra
of Young CSPNs
5.1 Introduction – ESO Time-series Objects & their obser-
vation
In March 2006 observations were carried out of three young H-rich (O star type) planetary
nebulae: Hen 2-138, Hen 2-131, and NGC 2392 (commonly known as the Eskimo Nebula).
The main aim of the run was to obtain time-series optical spectra over 3 nights of observing,
the data from which would be used to seek out structure within the stellar winds emanating
from the central stars of these nebulae; and to uncover the nature of any modulated
behaviour. The monitoring of such structural modulation would aid the understanding of
the possible causes of such behaviour, including the occurrence of non-radial pulsations
(NRPs) which it has been suspected may be a direct precursor of co-rotating interaction
regions (CIRs) which themselves create large-scale structure in the winds of massive OB
stars (Cranmer & Owocki 1996). Therefore any signs of modulated structure with the
outflow of these CSPNs would suggest further similarities between the behaviour of H-rich
CSPNs and OB stars.
161
5.1. Introduction – ESO Time-series Objects & their observation 162
Fig. 5.1. HST WFPC2 image of PN Hen 2-138, captured via the Hα filter:http://www.aip.de/groups/sternphysik/stp/PN/cdrom/images/
5.1. Introduction – ESO Time-series Objects & their observation 163
Fig. 5.2. HST WFPC2 image of PN Hen 2-131, captured via the Hα filter:http://www.aip.de/groups/sternphysik/stp/PN/cdrom/images/
5.1. Introduction – ESO Time-series Objects & their observation 164
Fig. 5.3. HST WFPC2 image of PN NGC 2392: the differ-ent colours of the image highlight different gases comprising the neb-ula: nitrogen (red), hydrogen (green), oxygen (blue), and helium (violet):http://www.stsci.edu/ inr/thisweek1/thisweek029.html
5.1. Introduction – ESO Time-series Objects & their observation 165
Table 5.1. Hen 2-138 central star parametersParameter Value Ref.
Sp. type Of (H-rich) Mendez et al. (1998)Teff 28000 ± 2000 K This studyLog g 2.9 ± 0.2 This studyMass 0.60 This studyLog (L/L⊙) 3.87 This studyDistance 3.5 kpc Zhang (1995)Radial velocity −47 km s−1 Schneider et al (1983)
5.1.1 Hen 2-138
The nebula possess a complicated knotted appearance, with bubble-like structures ar-
ranged in a fairly symmetrical manner about an overall elliptical morphology. The central
star of Hen 2-138 (HD 141969) has been analysed in the search for photometric varia-
tions as a result of positive results occurring in similar studies in other CSPNs (Hutton
& Mendez 1993): the variations found were on the time scale of hours, and were there-
fore similar to those found in the photometric observations of the central stars of IC 418
(Mendez et al. 1986) and IC 4593 (Bond & Ciardullo 1989). Both HD 141969 (the central
star of Hen 2-138) and HD 138403 (the CS of Hen 2-131) have exhibited fluctuations in
magnitude of between 0.10 and 0.15 mag over the timescale of hours. These four central
stars are also similar in other parameters: they all possess relatively low effective temper-
atures of between 27,000 and 40,000 K (Mendez et al. 1988, 1990) as well as radial velocity
variations (Mendez 1989; Mendez et al. 1990), and also changes in emission and P Cygni
profiles (Mendez et al. 1988, 1990; Mendez 1991).
5.1.2 Hen 2-131 & NGC 2392
These two planetary nebulae and their respective central stars HD 138403 (Hen 2-131) and
HD 059088 (NGC 2392) have previously been studied extensively with the aim of testing
the validity of radiatively driven wind theory (see Kudritzki et al. 1997; Pauldrach et al.
2003; Kudritzki et al. 2006).
A prime motivation was to see whether the plane-parallel models used, based upon
the model fitting of Balmer lines, can sufficiently match the observed wind profile with a
degree of success comparable to that previously achieved in similar modelling the winds
of O, B, and A stars.
Despite a lack of reliable CSPN distance measures, earlier efforts involved plotting the
5.1. Introduction – ESO Time-series Objects & their observation 166
positions of CSPNs upon the log g – log Teff diagram and comparing these to plots of post-
AGB tracks obtained via the log L – log Teff diagram: in this way the stellar masses could
be read in the log g – log Teff diagram, and hence the corresponding luminosities could
be calculated; also, with knowledge of de-reddened apparent magnitudes, stellar distances
could even be derived (Kudritzki et al. 1997). The results of this analysis seemed to echo
the success previously achieved with the CSPN results forming a relatively small scatter
about the wind-momentum–luminosity relation diagram for O, B and A supergiant stars,
but extrapolated back for the lower luminosities of the CSPNs.
An alternative modelling approach, based upon a homogeneous, spherically-symmetric,
radiatively-driven atmospheric outflow, involved solving hydrodynamic and nLTE prob-
lems concerning rate equations and radiative transfer (Pauldrach et al. 2003). These
problems are solved iteratively, whereby a synthesised spectrum is calculated and then
compared with the observed spectrum and, as necessary, subsequent adjustments are made
to stellar parameters (radius, terminal velocity, and then mass) in order to improve the
fit.
When this latter iterative technique was applied to spectra of the central stars of Hen
2-131 and NGC 2392, some interesting (and rather conflicting) results were thrown up.
The directly-measured terminal velocity of Hen 2-131, given at ∼ 500 km s−1 fits neatly
between post-AGB evolution tracks of masses 0.565 and 0.625 M⊙, and so seemingly
indicating a mass of ∼ 0.6 M⊙, but this mass should be consistent with a mass-loss rate
of ∼ 10−8 M⊙ yr−1, but is in fact estimated to be 100 times as much, and such a mass-loss
rate of ∼ 10−6 M⊙ yr−1 should only emanate from a central star of a mass ∼ 0.9 M⊙.
With NGC 2392, its measured terminal velocity (as similarly compared to the post-
AGB tracks) indicated a mass of ∼ 0.9 M⊙ but the observed mass-loss rate of ∼ 10−8
M⊙ yr−1 was too small for this large a mass, and conversely indicated a smaller mass of ∼0.6 M⊙.
Alternatively, taking the the mass-loss rates determined via the post-evolution mass-
luminosity tracks as a starting point, would seem to predict terminal velocities which differ
by a factor of 2 or 3 from the values obtained by direct measurement.
The observed UV spectra of Hen 2-131 provided an indication of the success of any
particular assumed parameter value through the direct comparison of the modelled profile
when superimposed upon that observed. With a preliminary mass (0.6 M⊙) derived from
the directly-measured terminal velocity, the subsequent mass-loss rate and hydrodynamical
5.2. European Southern Observatory 3.6 m Telescope & the HARPS Spectrograph 167
model was too low to be able to accurately match the observed profile, with the result
that the luminosity had to be increased as this had a direct bearing on the mass-loss
rate which itself had to increase in order for the model to better reproduce the observed
spectrum, while also adjusting the mass (up to 0.9 M⊙) in order to maintain the same
directly-observed terminal velocity.
With the UV spectrum of NGC 2392, however, as the initial mass-loss rate (and
resultant mass of 0.9 M⊙) was too high to match the observed spectrum and so had to
be lowered through the adjustment of the luminosity (and subsequent mass down to 0.6
M⊙) in order to match the observed spectrum.
However, other parameters were also taken from observed quantities, for example Teff
was derived from the ionisation equilibrium of Fe ions in the UV spectra, which for the
weak-winded NGC 2392 is 40,000 K. Its low terminal velocity of −400 km s−1 coupled with
its lowered luminosity (reduced in order to better match the model spectral profile with
that of the observed UV) resulted in a small radius of ∼ 1.5 R⊙, which together with the
measured v∞ gave a stellar mass of ∼ 0.4 M⊙ – less than half the ∼ 0.9 M⊙ mass that was
predicted earlier via the mass-luminosity relationship.
For Hen 2-131, the mass-luminosity relationship suggested a stellar mass of ∼ 0.6
M⊙for the measured terminal velocity of −500 km s−1 and temperature of 33,000 K, but
for these measured values the UV model under-predicted the mass-loss rate as compared to
the observed spectrum and so the luminosity needed to be increased to raise the observed
mass-loss rate leading to a much larger stellar radius of 5.5 R⊙, and hence an increase
of stellar mass from the M-L relationship-derived 0.88 M⊙ to an even larger 1.39 M⊙ –
almost at the Chandrasekhar limit.
When applied to the wind-momentum–luminosity relation diagram, the results if the
latter hydrodynamical analysis provide a narrower spread of plotted points about the
extrapolated wind-momentum–luminosity relation as defined by the more massive and
hotter stars.
5.2 European Southern Observatory 3.6 m Telescope & the
HARPS Spectrograph
The H igh-Accuracy Radial velocity P lanet Searcher (HARPS ) spectrograph was chosen
because of its high resolving power, R = 111,000 over the 4000-7000 A wavelength range,
5.2. European Southern Observatory 3.6 m Telescope & the HARPS Spectrograph 168
Table 5.2. Hen 2-131 & NGC 2392 central stars’ parametersParameter Hen 2-131 NGC 2392 Ref.
Sp. type Of Of Mendez et al. (1998)Teff [K] 32000 44000 Kudritzki et al. (2006)Log g 3.2 3.6 Kudritzki et al. (2006)Mass [M⊙] 0.71 0.86 Kudritzki et al. (2006)Log (L/L⊙) 4.07 4.30 Kudritzki et al. (2006)Distance [kpc] 3.3 2.8 Kudritzki et al. (2006)Radial velocity [km s−1] −1 +75 Schneider et al. (1983)
Table 5.3. ESO 3.6 m & HARPS specificationsParameter Value
Wavelength range 4000–7000 AResolving power, R 110,000Signal-to-noise, S/N ≥ 40
thus enabling the observer the opportunity to view and subsequently analyse spectral lines
at a different point in the wind. The clarity of the P Cygni profiles observed is aided by
the high signal-to-noise ratio, with S/N ≥ 40 for the 30 minute duration of the exposures.
Located at the La Silla observatory on the edge of the Atacama desert in northern Chile
and at an altitude of 2400 m above sea level, the 3.6 m telescope is equatorially-mounted
and uses a Cassegrain focus (f8) to direct light via towards the HARPS spectrograph. It
has a pointing accuracy to within 5 arcsec (RMS) and a PSF of ∼ 0.7-0.8.
The HARPS spectrograph is an eschelle spectrograph, contained within a vacuum
vessel which help to reduce the velocity drift otherwise caused by variations in temperature
and air pressure. It is fed by a pair of fibres, one of which collects the starlight while the
other is directed toward a Thorium-Argon lamp to record a reference spectrum.
5.2.1 Data Reduction Pipeline
The HARPS Consortium have developed software which allows for the entire data reduc-
tion procedure to be carried out in near real-time; the reduction depends on the observing
mode as well as the spectral type of the star – these parameters are received by the pipeline
from the FITS header information of the raw data.
Reduction results include:
• dark current values,
• order localisation,
5.2. European Southern Observatory 3.6 m Telescope & the HARPS Spectrograph 169
• flat fields,
• dispersion solution for calibrations;
• extracted spectra for all modes;
• precise radial velocity – for simultaneous Th reference only;
• cross correlation function – for simultaneous Th reference only.
The pipeline runs automatically for all spectra at the telescope with no intervention
required by the user; warning pop-up windows are handled by the support astronomer.
5.2.2 ESO Time-series Optical Data
The time-series data under investigation was taken with the 3.6m optical telescope at
the La Silla observatory in Chile, and the data collected upon the HARPS spectro-
graph, over three nights between March 24th and March 26th 2006 (BJD 2453818.67601
to 2453820.90567), with a total of 18 spectra being taken, 6 over each of the consecutive
nights.
Details of exposure times (UT and MJD), targets, and duration are listed in Table 5.4
Table 5.4: ESO La Silla observation log summary.
UT Date & Time (start) MJD (start) Target Exposure [s]
2006 March 24 00:02:28.611 53818.5139 NGC 2392 1800
00:33:30.717 53818.5354 NGC 2392 1800
01:04:29.464 53818.5569 NGC 2392 1800
01:35:13.489 53818.5783 NGC 2392 1800
02:06:02.195 53818.5997 NGC 2392 1800
02:36:53.142 53818.6211 NGC 2392 1800
03:23:03.749 53818.6527 Hen 2-131 1800
03:56:26.961 53818.6760 Hen 2-138 1800
04:28:46.776 53818.6983 Hen 2-131 1800
05:00:16.016 53818.7203 Hen 2-138 1800
05:31:59.367 53818.7422 Hen 2-131 1800
06:04:31.504 53818.7650 Hen 2-138 1800
06:48:41.041 53818.7955 Hen 2-131 1800
07:20:49.895 53818.8180 Hen 2-138 1800
cont. on next page
5.2. European Southern Observatory 3.6 m Telescope & the HARPS Spectrograph 170
Table 5.4 cont.
UT Date & Time (start) MJD (start) Target Exposure [s]
07:52:49.869 53818.8400 Hen 2-131 1800
08:24:26.479 53818.8621 Hen 2-138 1800
08:56:12.511 53818.8840 Hen 2-131 1800
09:27:32.849 53818.9060 Hen 2-138 1800
2006 March 24 23:53:08.599 53819.5073 NGC 2392 1800
2006 March 25 00:23:42.093 53819.5285 NGC 2392 1800
00:54:18.288 53819.5498 NGC 2392 1800
01:24:52.872 53819.5710 NGC 2392 1800
01:55:28.396 53819.5923 NGC 2392 1800
02:26:02.530 53819.6135 NGC 2392 1800
03:09:54.575 53819.6436 Hen 2-131 1800
03:42:20.360 53819.6663 Hen 2-138 1800
04:14:57.797 53819.6888 Hen 2-131 1800
04:47:49.226 53819.7118 Hen 2-138 1800
05:19:24.135 53819.7335 Hen 2-131 1800
05:50:59.656 53819.7556 Hen 2-138 1800
06:34:59.712 53819.7860 Hen 2-131 1800
07:06:29.371 53819.8081 Hen 2-138 1800
07:38:19.213 53819.8300 Hen 2-131 1800
08:09:45.773 53819.8520 Hen 2-138 1800
08:41:26.884 53819.8738 Hen 2-131 1800
09:12:59.965 53819.8959 Hen 2-138 1800
2006 March 26 00:02:33.378 53820.5138 NGC 2392 1800
00:33:10.742 53820.5350 NGC 2392 1800
01:03:45.048 53820.5562 NGC 2392 1800
01:34:18.601 53820.5775 NGC 2392 1800
02:04:52.147 53820.5987 NGC 2392 1800
02:35:28.409 53820.6199 NGC 2392 1800
03:22:15.952 53820.6522 Hen 2-131 1800
03:54:13.135 53820.6746 Hen 2-138 1800
cont. on next page
5.3. Time-Averaged Fast-Wind Characteristics 171
Table 5.4 cont.
UT Date & Time (start) MJD (start) Target Exposure [s]
04:28:22.441 53820.6981 Hen 2-131 1800
04:59:54.791 53820.7202 Hen 2-138 1800
05:31:57.055 53820.7423 Hen 2-131 1800
06:04:52.014 53820.7653 Hen 2-138 1800
06:48:15.745 53820.7953 Hen 2-131 1800
07:19:52.106 53820.8174 Hen 2-138 1800
07:51:38.468 53820.8393 Hen 2-131 1800
08:23:31.900 53820.8616 Hen 2-138 1800
08:55:19.142 53820.8835 Hen 2-131 1800
09:26:56.383 53820.9057 Hen 2-138 1800
All data for each of the three objects have been corrected for their respective system’s
Helio-centric radial velocity: −47 km s−1 for Hen 2-138; −1.2 km s−1 for Hen 2-131; +75
km s−1 for NGC 2392 (Schneider et al. 1983).
5.3 Time-Averaged Fast-Wind Characteristics
5.3.1 Variety of Absorption Lines
The spectrum is comprised of stellar lines and nebular emission – rest velocity He i lines,
metal absorption profiles lines – blue-shifted absorption, P-Cygni profiles, and nebular
lines, see Figure 5.5.
The evidence for stellar wind activity is mainly attributed to the appearance of a
significant P Cygni line for the He i λ 5875.57 line – which corresponds to the 23pP0 - 33D
shift. Further information about the physical nature of the wind can be extracted from
a study of UV data, and to this end a variety of wind lines have been taken from FUSE,
IUE and HST spectra, see Figure 5.6.
5.3. Time-Averaged Fast-Wind Characteristics 172
5.3.2 Ion species: Hen 2-138
Among these are certain low-ionisation species, such as C ii λ 1334.53, Al iii λλ 1854.72,
1862.79, Mg ii λλ 2795.53, 2802.70 and C iii λ 1175.66, and also the high-ionisation species
S iv λλ 1062.66, 1072.97, Si iv λλ 1393.76, 1402.77 and C iv λλ 1548.20, 1550.77. Notable
absences from the range of identifiable lines are Nv λλ 1238.82, 1242.80 and O vi λλ 1031.93,
1037.62 which are often ascribed to shocked gas in hot star winds.
Velocity space spectra for each of the ions shows a disparity in the blue wind-shifted
velocity of these wind lines – those of the lower ions show blueward absorption in the
range ∼ −100 – −300 km s−1 whereas the higher ions are blueward shifted to lie within
the range ∼ −500 – −700 km s−1. Altogether the lines show strong, often saturated,
optical depths in the low to intermediate velocity range, and from these UV lines, as well
as the P Cygni of He i λ 5875.62, one would conclude that the wind of Hen 2-138 is a dense
and comparatively slow moving one. The denseness of the wind is further emphasised if
one examines the spectra of the Si iii λ 1300 triplets – see Figure 5.7 – lines which form in
particularly dense atmospheres and which here show blueshifts of between ∼ −60 km s−1
and −80 km s−1, indicating the presence of the radial outflow right at the base of the wind.
5.3.3 SEI Model Fits – Hen 2-138
In order to uncover some of the physical parameters of Hen 2-138, the Sobolev with Exact
Integration (SEI) method was employed, but due to the lack of extensive UV time series
data, the code will only be applied to single exposures as an suggestive representation
of an ‘average’ moment. As in the two previous chapters the underlying photospheric
spectrum has been derived from the TLUSTY plane-parallel grid of models – specifically
that for Teff = 27,500 K and log g = 3.00 – and this photospheric input Gaussian (repre-
senting the underlying absorption profile) is rotationally broadened by 100 km s−1. The
resultant models are converted into the product of M and the (specific) ionisation fraction
qi, Mqi(w), and the mean < Mqi >, averaged over the 0.2 ≤ w ≤ 0.9 normalised velocity
range, is subsequently derived and presented for each ion species modelled.
Presented in Figure 5.8 are the SEI model fits for the ions Si iv λ 1393.76, C iv λ 1548.20,
S iv λ 1072.97, and Al iii λ 1854.72. The first thing to note is that the higher ionisation
species of Si iv and C iv require a higher terminal velocity parameter of −700 km s−1
in order for the models to be derived, but the lower ionisation species of Al iii and S iv
5.3. Time-Averaged Fast-Wind Characteristics 173
Table 5.5. SEI-derived mass-loss and wind ionisation parametersIon < Mqi > < qi >
[M⊙ yr−1]
Al2+ 7.7 ×10−10 6 ×10−3
S3+ 2.5 ×10−9 2 ×10−2
Si3+ 2.4 ×10−10 2 ×10−3
C3+ 1.1 ×10−10 9 ×10−4
require a terminal velocity parameter of only −300 km s−1. Assuming a solar abundance
and using the parameters detailed in Table 1, and derived via CMFGEN analysis carried
out by Miguel Urbaneja (described below), the models obtain values for the averaged
mass-loss rate – ionisation fraction product < Mqi >, which are listed in Table 5.5.
Another general point is that the SEI models all underestimate the strengths of the
ionisation component of the UV P Cygni profiles for Hen 2-138, this despite the adoption
of significantly slow wind laws with the acceleration parameter β = 3.00.
Al iii λ 1854.72
As the broad absorption profile of the blue component of the C iv doublet does not
present a clear blue edge from which one would normally measure the terminal velocity of
the outflow, then the much more clearly defined blue edge of the Al iii λ 1854.72 P Cygni
was used to obtain a measure of the terminal velocity which (to the nearest 10 km s−1)
was measured to be v∞ = −300 km s−1. The wind acceleration parameter, β, has to be
raised to a relatively high value of β = 3.00 (and hence describes a slowly accelerating
velocity law) in order for the projected P Cygni emission peak of SEI model to approach
that of the underlying spectra. These velocity law parameters of v∞ and β are applied to
a photospheric Gaussian profile with a FWHM of ∼ of 200 km s−1 and a central optical
depth of 0.500. Despite the strong P Cygni shape of the profile the absorption trough does
drop to saturated levels between w ∼0.6 and w ∼0.8; also the model predicts excessive
forward scattering which prevents accurate modelling across the width of the absorption
trough. The optical depth is high across almost the entire trough, increasing from 2.8 at
w ∼ 0.2, increasing to 4.6 at w = 0.8, before dropping rapidly to a low of 0.8 at w > 0.9.
5.3. Time-Averaged Fast-Wind Characteristics 174
S iv λ 1072.97
An SEI model fit has been achieved for the red component of the S iv λλ 1062.66, 1072.97
doublet by applying a similar velocity law, v∞ = −300 km s−1, β = 3.00 to a photospheric
Gaussian profile with FWHM ∼325 km s−1 and a central optical depth of 0.850; an in-
creased turbulence/smoothing parameter of vturb = 0.16 is required to align the blue edge
of the model to that of the broad spectral absorption trough. The spectral absorption pro-
file approaches saturation between w ∼0.6 and w ∼0.8, and also the model also predicts
excessive forward scattering across the entire absorption range; again the optical depth is
therefore high across the entire width of the absorption and rises from 2.2 at w ∼ 0.2 to
a maximum of 5.8 at w = 0.85 before dropping back to 2.0 towards the blue edge (w >
0.9).
Si iv λ 1393.76
In applying the same velocity law parameters of v∞ = −300 km s−1 and β = 3.00 (upon
an input photospheric Gaussian of FWHM ∼ 575 km s−1) for the blue component of
the S iv λλ 1393.76, 1402.77 it became clear that this terminal velocity did not allow the
blue edge of the SEI model to match that of the spectral absorption trough underneath,
and it was through a trial-and-error process of gradually increasing the velocity to v∞ =
−700 km s−1 that an alignment was achieved. The absorption of the profile approaches
saturation between w ∼0.2 and w ∼0.5, where the blue edge occurs and from where the
profile then becomes progressively shallower: this is reflected in the optical depths of the
model which rapidly increase from 2.4 at w ∼0.2 to a maximum of 7.0 at w = 0.5 (this
range is also where the model shows excess forward scattering); the optical depth then
drops off sharply to a much lower level of ∼0.4 for w > 0.6.
C iv λλ 1548.20, 1550.77
The broad blue and red components of C iv λλ 5148.20, 1550.77 are both saturated and
blended with each other to an extent that the emission peak of the blue component has
been removed by the absorption of the red. This makes this doublet extremely difficult
to model, however a vague degree of alignment was achieved, but again with the higher
terminal velocity of v∞= −700 km s−1 (β = 3.00, and vturb= 0.15 to allow for the broadness
of the profile, the input Gaussian of which has a FWHM of ∼ 400 km s−1). The high
5.3. Time-Averaged Fast-Wind Characteristics 175
saturation of the absorption and excess forward scattering are reflected in the optical
depths of the model which rise from 3.0 at w ∼0.2 to 6.0 at w = 0.6, and then sharply
drop to a low of 0.1 at w = 0.75, rising again to between 1.0 and 1.5 for w > 0.9.
5.3.4 CMFGEN Analysis of Hen 2-138
In order to obtain more fundamental parameters from the time-averaged UV spectra, it
has been modelled by Miguel Urbaneja (IfA, Hawai’i), using the unified non-LTE, line-
blanketed model atmosphere code CMFGEN (Hillier & Miller 1998). The model is defined
by the stellar radius, the luminosity, the mass-loss rate, the wind terminal velocity, the
stellar mass, and by the abundances of the species included in the calculations. The code
does not solve for the hydrodynamical structure and so requires the velocity field has to
be defined. To this end, the output of a plane-parallel model (such as that provided by
TLUSTY) is used to define the pseudo-static photosphere, connected to just below the
solar point of a β-type velocity law – such as that used in SEI – to describe the wind
regime.
The effective temperature of the system is derived from the ionisation balance of He,
where only the He i lines of the spin system and those He ii lines present in the optical
are used. In this case He ii lines react strongly to temperature changes of ± 1000 K,
whilst the He i lines remain unaffected. The surface gravity is determined by the fitting
of the Balmer lines series. More weight is given to the higher lines as stellar wind effects
and contamination by ionised gas are less important. The photospheric structure is linked
to the stellar mass and so different values would result in changes. These would be very
small, however, for this target object.
The final model is shown in Figure 5.9 where most of the features of the FUV/UV
spectrum are successfully reproduced. However, the wide absorption troughs of the Si iv
and C iv profiles are not well matched, and it under-predicts the strengths of the Al iii
lines. Low ionisation species require a lower effective temperature but then it is found
that this will not produce the observed He i /He ii ionisation balance; conversely, high
ionisation features present in the optical spectrum, such as the O iii and C iv lines,
require a higher effective temperature, but again, that would not successfully reproduce
the correct ionisation balance.
This two-temperature requirement is consistent with a similar situation in the SEI
modelling: v∞= −300 km s−1 is adequate for the Al iii and S iv (red component); whereas
5.3. Time-Averaged Fast-Wind Characteristics 176
v∞ = −750 km s−1 is required for the S iv and C iv lines.
Since these modelling codes assume spherically-symmetric winds, the problems ob-
served here in being forced to adopt different parameters to be able to match both high
and low ionisation lines, coupled with discrepancies in matching the absorption and emis-
sion strengths of P Cygni profiles, would seem to suggest that the wind and its terminal
velocity and mass-loss are latitude-dependent. Low velocity, low ion species forming in
the cooler equatorial regions of an asymmetric outflow that is viewed almost pole-on –
the higher speed, high ions of Si iv and C iv are being driven out from the hotter polar
regions of the outflow.
For a v∞ of 300 km s−1, Teff = 29,000 K, adopted central star mass of ∼ 0.6 M⊙, and
a log(L/L⊙) ∼ 3.9, the CMFGEN model yields a mass-loss parameter log Q ∼ -11.45 dex
(where Q = M (R⋆v∞)−1.5) and hence a mass-loss rate of ∼ 1.2 ×10−7 M⊙ yr−1. The
model is for a smooth wind with clumping being unconstrained here, but it is noted as
being very low. The wind momentum value, log (M⊙v∞R⋆0.5), of ∼ 26.6 dex is within
the scatter of the wind momentum-luminosity relation observed/derived for CSPNs and
predicted by line-driven wind theory (see e.g. Kudritzki et al. 2006); although in the CSPN
region alone, there is not a convincing relation between wind momentum and luminosity.
In comparing the CMFGEN-derived mass-loss rate with those derived from the em-
pirical line SEI models results < Mq >, the empirical analyses would suggest that none
of the SEI-modelled ion species are dominant in the wind, however in the CMFGEN base
model that S3+ and Si3+ ionisation fractions are dominant in the wind (i.e. ∼ 90%):
this would suggest that either the CMFGEN-derived mass-loss rate is over -estimated or
the SEI-derived product of Mq is under -estimated. For a mass-loss rate of ∼ 1.2 × 10−7
M⊙ yr−1, the corresponding ion fractions are also listed in Table 5.5.
5.3. Time-Averaged Fast-Wind Characteristics 177
Fig. 5.4. Diagram of the ESO HARPS spec-trograph system, courtesy of the ESO website:http://www.eso.org/sci/facilities/lasilla/instruments/harps/inst/description.html
5.3. Time-Averaged Fast-Wind Characteristics 178
Fig. 5.5. Mean ESO optical spectral lines of photospheric, fast wind and nebularegions of Hen 2-138.
Fig. 5.6. Mean far UV spectral lines depicting fast wind features from FUSE &IUE data of Hen 2-138.
5.3. Time-Averaged Fast-Wind Characteristics 179
Fig. 5.7. Hen 2-138 UV spectrum (IUE) showing blueward shifted Si iii triplets– with Si iii singlet at 1312 A also shown – the vertical dashed lines indicate thespectral rest positions.
5.3. Time-Averaged Fast-Wind Characteristics 180
Fig. 5.8. SEI fits to the Hen 2-138 UV P Cygni profiles of (left to right, topto bottom: Si iv λ 1394, C iv λ 1548, S iv λ 1073, and Al iii λ 1855. The largerpanels display the SEI model fit overlaid upon the observed spectra, and thesmaller panels depict the input photospheric spectra (right) and the derived radialoptical depth profile shown as a function of normalised velocity (left). The twohigher ionisation species (above) require a higher terminal velocity of 700 km s−1,whereas the two lower ionisation species (below) only require a terminal velocityof 300 km s−1.
5.3. Time-Averaged Fast-Wind Characteristics 181
Fig. 5.9. CMFGEN model fits for Hen 2-138
5.3. Time-Averaged Fast-Wind Characteristics 182
Fig. 5.10. Mean ESO optical resonance lines of photospheric, fast wind, andnebula regions of Hen 2-131.
5.3.5 Ion Species - Hen 2-131
The optical spectra of Hen 2-131 also includes the low-ionisation species, such as C ii λ 1334.53,
Al iii λλ 1854.72, 1862.79, Mg ii λλ 2795.53, 2802.70 and C iii λ 1175.66, as well as the high-
ionisation species S iv λλ 1062.66, 1072.97, Si iv λλ 1393.76, 1402.77 and C iv λλ 1548.20,
1550.77. The blue edges of the stronger absorption troughs of the species appear within a
−200 – −500 km s−1 range.
Again, as with Hen 2-138, the shocked gas wind lines of Nv λλ 1238.82, 1242.80 and
O vi λλ 1031.93, 1037.62 are absent. However the P v λ 1117.98 component – not present
in the UV spectra of Hen 2-138 – can be seen in the spectra, although its emission peak
is not as strong as its blueward absorption trough.
As with the outflow of Hen 2-138, the Si iii λ 1200 triplet is examined for any indications
of blueshift and in the UV spectrum of Hen 2-131 the triplet lines of are blueshifted by a
far greater velocity than those of Hen 2-138: in Hen 2-131 the blue shift is between −160
and −220 km s−1, which in contrast to the outflow of Hen 2-138, would suggest a less
dense wind, but slow-moving.
5.3. Time-Averaged Fast-Wind Characteristics 183
Fig. 5.11. Mean far UV spectral lines depicting fast wind features from FUSE& IUE data of Hen 2-131.
Fig. 5.12. Hen 2-131 UV spectrum (IUE) showing blueward shiftedSi iii triplets - with Si iii singlet at 1312 A also shown - the vertical dashedlines indicate the spectral rest positions.
5.3.6 SEI Model Fits - Hen 2-131
P v λ 1117.98
The blue component of the P v λλ 1178.98, 1128.01 doublet is modelled with a terminal
velocity of v∞ = −400 km s−1 (Kudritzki et al. 2006) – upon a Gaussian input profile of
FWHM = 250 km s−1, central optical depth of 0.800 – and a similar wind law β factor of
3.00 (vturb was initially given the low value of 0.05 and it was found that this did not need
to be increased in order to align the blue edge of the absorption). The high β appears to
over predict the emission peak of the profile but not excessively, and indeed the apparent
emission of the profile is unusually weak. Also the forward scattering as predicted by the
5.3. Time-Averaged Fast-Wind Characteristics 184
Fig. 5.13. SEI model fits to the Hen 2-131 P Cygni resonance profiles ofP v λ 1118, S iv λ 1073, Si iv λ 1394, and Al iii λ 1855.
model does not overlap with the lower velocity absorption but the edge of one appears to
coincide with the edge of the other. This being so the optical depths adopted to model the
absorption profile are reasonable high despite the profile being unsaturated: rising from
∼2.0 at w ∼0.20 to 5.6 at w ∼0.50; the optical depths are then much lower across the
bluer half of the trough, dropping towards 1.0 at w ∼0.75 and then less than half again
for w >0.90.
S iv λ 1072.97
The P Cygni-like red component of the S iv 1062.66, 1072.97 doublet is highly saturated in
absorption to the extent that it flattens out along the zero-flux level. This high saturation
cannot be replicated in the model (v∞ = −400 km s−1, β = 3.00, vturb = 0.16, upon a
photospheric Gaussian of FWHM = 300 km s−1, central optical depth = 0.650), which for
the full extent of the absorption trough is hampered by the forward scattering component.
5.3. Time-Averaged Fast-Wind Characteristics 185
The optical depths therefore are necessarily high in order to bring the model down as far as
to meet the forward scattering and are of the order of ∼3.6 for ∼ 0.20 > w > 0.60, further
increasing to a maximum of 4.8 at w ∼0.80, and falling slightly to 4.0 at the terminal
velocity.
Si iv λ 1393.76
The modelling of the P Cygni of the blue component of the Si iv 1393.76, 1402.77 doublet
(input Gaussian: FWHM = 325 km s−1, central optical depth of 1.100), could only be
achieved by increasing the terminal velocity to v∞ = −600 km s−1 while still retaining β
= 3.00 (and increasing vturb to 0.15 to align the model with the slope of the blue edge).
Whether this indicates a similar two-component outflow, such as described above for
Hen 2-138, is uncertain, as the terminal velocity required for all other modelled P Cygni
profiles for Hen 2-131 was that of 400 km s−1, as assigned by Kudritzki et al. (2006). As
the absorption approaches near saturation levels in the range 0.30 > w > 0.70 the optical
depths again can only bring down the model’s flux level to that of the encroaching forward
scattering in this velocity range where the optical depth range from a minimum of 3.4 to
a maximum of 4.0; for w > 0.70 the optical depths fall to ∼1.5 up to w = 0.90 and then,
as the flux rises toward the continuum level, drop to 1.0 at terminal velocity.
Al iii λ 1854.72
The unsaturated Al iii 1854.72 has had its input Gaussian profile (FWHM = 200 km s−1,
central optical depth = 0.200) modelled using a wind law (similar to that used for the
unsaturated P v profile) of v∞ = −400 km s−1, β = 3.00, and the low vturb = 0.05. The
lack of saturation has not brought the flux levels within the level of the model’s forward
scattering prediction, therefore the optical depths adopted more accurately reflect the
absorption of the profile: from ∼2.0 at w ∼0.20 they drop to 0.8 at w = 0.45, before
increasing to a maximum of 1.4 at w = 0.50, then falling slightly towards 0.8 at w = 0.80
from where the optical depth drops again, but sharply, to an average of ∼0.2 for w > 0.80.
5.3.7 Ion Species - NGC 2392
Here there are the low-ionisation species, such as C ii λ 1334.53, Al iii λλ 1854.72, 1862.79,
Mg ii λλ 2795.53, 2802.70 and C iii λ 1175.66, and the high-ionisation species S iv λλ 1062.66,
1072.97, Si iv λλ 1393.76, 1402.77 and C iv λλ 1548.20, 1550.77. Again, like similar species
5.3. Time-Averaged Fast-Wind Characteristics 186
Fig. 5.14. Mean ESO optical resonance lines of photospheric, fast wind, andnebula regions of NGC 2392.
of Hen 2-131, the blue edges of the stronger species appear within a −200 – −500 km s−1
range.
Unlike the UV spectra of Hen 2-138 and Hen 2-131, the doublets of Nv λλ 1238.82,
1242.80 and O vi λλ 1031.93, 1037.62 are present and would therefore indicate the presence
of shocked gas in the wind. Also, as in the spectra of Hen 2-131, the P v λ 1117.98, 1128.01
doublet is also present.
The Si iii λ 1200 triplet – seen in Figure 5.16 – appears to be blueshifted only by
between −10 and −30 km s−1, which is even slower than that measured for Hen 2-138, but
the examination of the blue-shifted triplet is hampered by the appearance of rather weak
absorption lines – not nearly as strong as the similar lines of the other two ESO objects –
and it is difficult to pick out the absorption profiles from the noise of the continuum, despite
the triplet rest wavelength positions being marked. The small blueshift of the triplet would
indicate a dense wind, but the shallowness of the absorption lines, particularly in both
the ESO optical data, as well as the lack of strongly saturated UV profiles from IUE and
FUSE would indicate a relatively weak wind.
5.3. Time-Averaged Fast-Wind Characteristics 187
Fig. 5.15. Mean far UV spectral lines depicting fast wind features from FUSE& IUE data of NGC 2392.
Fig. 5.16. NGC 2392 UV spectrum (IUE) showing blueward shiftedSi iii triplets - with Si iii singlet at 1312 A also shown - the vertical dashedlines indicate the spectral rest positions.
5.3.8 SEI Model Fits - NGC 2392
O vi λ 1031.93
With a wind terminal velocity of v∞ = −400 km s−1 (Kudritzki et al. 2006), the strong P
Cygni profile of the blue component of the O vi λλ 1031.93, 1037.62 doublet was modelled
upon a Gaussian photospheric input absorption of FWHM = 200 km s−1, and a central
optical depth of 0.400; again the velocity law β acceleration parameter is set as high as
3.00 in order to match the high emission peak of the profile, with vturb = 0.10 to align the
model to the slope of the blue edge of the absorption. Although the profile’s absorption is
not saturated it does present a flattened trough and so between w ∼0.30 and w ∼0.60 the
5.3. Time-Averaged Fast-Wind Characteristics 188
Fig. 5.17. SEI model fits to the NGC 2392 P Cygni resonance profiles ofO vi λ 1032, Nv λ 1239, C iv λ 1548, and P v λ 1118.
spectra does fall beneath the model’s level of forward scattering, and as such, the optical
depth levels cannot push the profile of the model as far as the underlying absorption would
require: the optical depth rises from 3.2 at w = 0.30 to a high of 4.4 at w = 0.55; beyond
the excessive forward scattering, 0.60 < w < 0.90 the optical depth drops to ∼2.4 and
then sharply drops again to 0.2 for w >0.90.
Nv λ 1238.82
Using similar velocity law parameters (v∞ = −400 km s−1, β = 3.00, vturb = 0.10), the
blue component of the Nv λλ 1238.82, 1242.80 doublet had also been modelled (upon
a photospheric Gaussian input profile of FWHM = 250 km s−1, with a central optical
depth of 1.15), but despite the high β factor, the model falls short of the emission peak
presented in the P Cygni profile. As with the previous model, although the absorption
is not saturated, the more redward side of the spectral trough requires a deeper optical
5.3. Time-Averaged Fast-Wind Characteristics 189
depth than can be allowed by the excessive forward scattering component of the model,
affecting the absorption profile in the region ∼ 0.50 > w >∼ 0.30 in which the optical
depths of the model range between 3.4 and 4.8 (at w = 0.35). Further towards the blue,
i.e. w > 0.60, the optical depth remains of the order of ∼ 1.0 as the absorption trough
becomes shallower, with no definite edge.
C iv λ 1548.20
The blue component of the C iv λλ 1548.20, 1550.77 doublet presents a noticeably narrow
absorption trough, so much so that using the velocity law parameters of v∞= −400 km s−1,
β = 3.00, vturb = 0.10 as for the above NGC 2392 P Cygni profiles (upon an Gaussian
photospheric input profile of FWHM = 200 km s−1, central optical depth = 1.00), the
model predicts a broader absorption trough; also the high emission peak of the profile is
much underestimated by the model despite the high β factor of 3.00. The saturation of
the absorption in the region ∼ 0.30 > w >∼ 0.50 is again affected by excessive forward
scattering where the optical depths range from 3.4 to a maximum of 5.0 (at w = 0.35). In
the region w > 0.60 the absorption trough possesses a steep edge; the shallowness of the
trough further blueward is reflected in the low optical depth of the model of ∼ 0.2 as the
absorption merges into the continuum.
P v λ 1117.98
The unsaturated profile of the Pv λλ 1117.98, 1128.01 doublet of NGC 2392 is noticeably
weak, with the blue component comprising a shallow absorption trough and a significantly
small emission peak, but even so, is only marginally overestimated by the high β = 3.00
factor of the adopted wind law (again with v∞= −400 km s−1, but a slightly reduced vturb
of 0.07 to match the blue edge slope, upon a Gaussian photospheric input profile of FWHM
= 200 km s−1, central optical depth = 0.80). The relatively shallow, unsaturated nature
of the absorption prevents the level of forward scattering, as predicted by the model, from
overlapping the trough; therefore the levels of optical depth adopted in order to model
the absorption reflect the optical depths of the spectral profile much more accurately than
those of the more saturated profiles described above. The optical depths are highest at
∼1.6 at w ∼0.20, then drop to ∼0.9 for 0.30 > w > 0.50, and then drop down to marginally
fluctuate around 0.2 for w > 0.50 as the absorption again starts to merge into the level of
the continuum.
5.4. Time Variable Characteristics of the CSPN Winds 190
Fig. 5.18. Three 18 exposure over-plots of the He i λ 5876 line for (l-r) Hen2-138, Hen 2-131, NGC 2392, the individual exposures, taken over ∼ 2.2 days,are plotted in red, and the mean profile is overlaid in black, so as to furtheremphasise the variable nature of the P Cygni profile.
5.4 Time Variable Characteristics of the CSPN Winds
5.4.1 Equivalent Width Measurements – Hen 2-138
After studying the time-averaged data of the central star winds of these three objects, the
more time-dependent nature of the PNs winds can be explored. The initial indications
of the variable nature come from time-dependent variations in the P Cygni profile of the
He i λ 5875.62, see Figure 5.18. Here 18 time-series exposures for each object, obtained over
∼ 2.2 days are simultaneously plotted in red with the mean spectrum superimposed upon
the others in black, thereby allowing the extent of the variability to be estimated. The
absorption profile shows variation up to an extent of ∼ −200 km s−1. Also, time-variable
changes of the optical lines of He i λ 4026.19, He i λ 4471.48, and the more deep-bedded
C iv λ 5801.33 are studied, lines which show behaviour more akin to changes in lower
regions close to the photosphere than in the more developed wind.
More quantitative evidence can be obtained from equivalent width measurements of
the profiles, and these are shown in Table 5.6. The maximum and minimum EW mea-
surements for both absorption troughs and emission peaks for the He i λ 5875.62 P Cygni
are listed (along with the mean EW and the standard deviation of the EW range) as
measured between the given wavelengths, which indicate the estimated extremities of the
troughs/peaks before merging back into the continuum. Also listed are the max./min. EW
measurements (along with mean EW and SD) for the He i λ 4026.19 and He i λ 4471.48 op-
tical lines as well as the deep-seated C iv λ 5801.33 line. As can be seen in the table the
5.4. Time Variable Characteristics of the CSPN Winds 191
Table 5.6. Hen 2-138 equivalent width measurements [A]Spectral Line Wavelength Range [A] Min – Max Mean SD Max % Diff.
He i λ 4026 4020.0 – 4030.0 a. 0.59 – 0.78 0.68 0.06 32He i λ 4471 4465.5 – 4472.0 a. 0.58 – 0.77 0.67 0.06 33He i λ 5876 5870.0 – 5874.4 a. 0.45 – 0.78 0.59 0.09 71He i λ 5876 5874.3 – 5880.0 e. 0.48 – 0.91 0.75 0.11 88C iv λ 5801 5795.0 – 5804.0 a. 0.29 – 0.37 0.33 0.02 27
He i λ 5875.62 profile shows the greatest variation in EW, varying between ∼ 0.45A and
0.78A in its absorption trough and between ∼ 0.48A and 0.91A in its emission peak. It
has also been observed that these variations are correlated between the absorption and
emission sections in that they vary together: the deepest absorption troughs are accom-
panied by the strongest emission components, and likewise for the shallowest/weakest of
each. The other (non-P Cygni) optical lines also exhibit variable EW measurements but
not quite to the extent of the aforementioned P Cygni profile: the absorption trough of
He i λ 4026.19 varies between ∼ 0.59A and 0.78A, that of He i λ 4471.48 varies between
0.58A and 0.77A; the deep-seated C iv λ 5801.33, also in absorption, varies in EW (al-
though to a lesser extent) between 0.29A and 0.37A.
5.4.2 Equivalent Width Measurements – Hen 2-131
The P Cygni profile of He i λ 5875.62 as observed within in the outflow from the central star
of Hen 2-131 is much less even distributed between its absorption trough and its emission
peak: whereas the EWs of absorption/emission of this line in Hen 2-138 are reasonably
similar, the emission peak of He i λ 5875.62 is much higher and its EW much greater than
that of the absorption trough, the variation in EW in the emission peak is roughly five
times that of the absorption trough, varying between ∼ 0.51A and 0.90A, as opposed to
the emission peak where the EW varies between ∼ 3.66A and 5.68A. Where the lines
He i λ 4026.19 and He i λ 4471.48 existed only in absorption in the outflow of He 2-138,
in the outflow of Hen 2-131 they both exhibit variable absorption troughs and emission
peaks: for the He i λ 4026 line the EW varies between ∼ 0.29A and 0.47A in absorption,
and between ∼ 0.02Aand 0.17Ain emission; for the He i λ 4471 line the EW varies between
∼ 0.30A and 0.58A in absorption, and between ∼ 0.42A and 0.67A in emission. The deep-
seated C iv λ 5801 line only shows an absorption trough which itself varies in EW between
∼ 0.23A and 0.49A.
5.4. Time Variable Characteristics of the CSPN Winds 192
Table 5.7. Hen 2-131 equivalent width measurements [A]Spectral Line Wavelength Range [A] Min – Max Mean SD Max % Diff.
He i λ 4026 4021.0 – 4025.8 a. 0.29 – 0.47 0.38 0.04 64He i λ 4026 4025.8 – 4026.4 e. 0.02 – 0.17 0.08 0.04 682He i λ 4471 4466.5 – 4471.0 a. 0.30 – 0.58 0.46 0.07 92He i λ 4471 4471.0 – 4476.2 e. 0.42 – 0.67 0.58 0.11 58He i λ 5876 5868.5 – 5874.8 a. 0.51 – 0.90 0.72 0.12 76He i λ 5876 5874.7 – 5881.5 e. 3.66 – 5.68 4.75 0.54 55C iv λ 5801 5796.5 – 5803.2 a. 0.23 – 0.49 0.34 0.08 110
Table 5.8. NGC 2392 equivalent width measurements [A]
Spectral Line Wavelength Range [A] Min – Max Mean SD Max % Diff.
He i λ 4026 4020.0 – 4033.0 a. 0.49 – 0.76 0.58 0.07 55He i λ 4471 4468.5 – 4474.5 a. 0.19 – 0.34 0.24 0.04 82He i λ 5876 5871.8 – 5878.5 a. 0.20 – 0.56 0.38 0.10 173C iv λ 5801 5800.7 – 5804.5 e. 0.07 – 0.13 0.09 0.02 79
5.4.3 Equivalent Width Measurements – NGC 2392
In the outflow of NGC 2392, the three He i lines all appear in absorption only – even the
He i λ 5875.62 line appears to show only an absorption trough: the region to the immediate
right of the absorption trough may be ever so slightly raised (in terms of flux) above the
continuum level but it is too subtle a change to be properly quantifiable. Any wind
emanating from the central star must be very weak indeed. Despite the lack of significant
P Cygni profiles in the helium lines, they do exhibit variability: He i λ 4026.19 varies in
EW between ∼ 0.49Aand 0.76A, He i λ 4471.48 varies between ∼ 0.19Aand 0.34A; but the
greatest variation in EW is shown in the He i λ 5875.62 wind line, between ∼ 0.20A and
0.56A. Of the metal lines, C iv λ 5801.33 shows the greatest relative variability: between
0.07A and 0.13A.
5.4.4 Time Variance Spectra (TVS) – Hen 2-138
All optical absorption lines of potentially significant variability were submitted to the
Time Variance Spectra (TVS) analysis algorithm with the aim of singling out those lines
which show a significant level of variability and thus require further investigation: only
those with considerable activity above the TVS confidence level line would perhaps reveal
a periodic frequency in later Fourier analysis.
After studying the time-averaged qualities of the central star winds of these three
5.4. Time Variable Characteristics of the CSPN Winds 193
objects, now the time-dependent nature of the PNs’ winds can be explored. The higher
wind He i λ 5875.62 line and the more photospherically dominated lines of He i λ 4026.19,
He i λ 4471.48 and the much more closely-photospheric, deep-seated C iv λ 5801.33 are now
subjected to the more rigorous time-variance analysis of the TVS algorithm.
In He i λ 5875.62 there is a clearly strong TVS response from both the absorption and
emission components of the P Cygni profile, with the absorption variance extending out to
∼ −200 km s−1 blueward; slightly further than the redward emission, the variance of which
extends to between ∼ +100 km s−1 and +150 km s−1. A broad absorption enhancement
appears during the 2nd night’s data but the extent of the observation is not long enough
to be able to discern whether this forms part of a migrating DAC, such as those observed
in the UV spectra of OB stars, or indeed as observed within the FUV data of NGC 6543
as discussed in Chapter 3 of this thesis (and also by Prinja et al. 2007).
The near-photospheric lines also show variability, but not quite to the extent of the
higher wind line: the TVS profile only extends to ∼ ±100 km s−1 above the 95% confidence
line. Also in both the He i λ 4026.19 and the He i λ 4471.48 lines the variability of the
profiles is revealed to be on a scale of hours by strong blue-to-red features appearing within
the 3rd night’s data, as seen in the uppermost greyscale strip, and hence are not correlated
with the 2nd night’s enhanced absorption component in He i λ 5875.62. An outward flowing
wind – where absorption enhancements (as with those of NGC 6543) would be expected
to migrate from red-to-blue – is seemingly not detected in the deeper near-photospheric
regions. Within the TVS profiles for the photospheric lines the response is stronger in the
redward ‘half’ of the TVS than in the blueward ‘half’, as well there being a drop in the
TVS response at about the rest velocity. The localised structures observed migrate across
the absorption troughs in an estimated 0.3 – 0.4 days. The EW of these profiles can vary
by as much as ∼ 25%. Similar TVS features are observed in the C iv λ 5801.33 line, which
is narrower than the He i lines – close to the projected rotational velocity – ±100 km s−1
– and hence are probably formed much closer to, or even at the photosphere.
Table 5.9 describes the extents in velocity of the varying absorption and emission
feature of the four lines under TVS analysis.
5.4.5 Time Variance Spectra (TVS) – Hen 2-131
The ESO time-series variance studies of a range of photospheric resonance lines from the
central star of PN Hen 2-131 are presented along with their accompanying greyscales:
5.4. Time Variable Characteristics of the CSPN Winds 194
Table 5.9. Hen 2-138 TVS velocity rangesSpectral Line TVS Velocity Range [km s−1]
He i λ 4026 −175 – +125He i λ 4471 −175 – +150He i λ 5876 −250 – +125C iv λ 5801 −75 – +125
Table 5.10. Hen 2-131 TVS velocity rangesSpectral Line TVS Velocity Range [km s−1]
He i λ 4026 −200 – +100He i λ 4471 −200 – +125He i λ 5876 −325 – +125C iv λ 5801 −125 – +125
the TVS analysis of He i λ 4026.19 shows a response above the 95% continuum line be-
tween −200 and +100 km s−1; the He i λ 4471.48 line between −200 and +125 km s−1;
the wind line of He i λ 5875.62 has a response between −325 and +125 km s−1; and the
deep-photosperic C iv λ 5801.33 line also, in the range of ±125 km s−1, see Table 5.10.
5.4.6 Time Variance Spectra (TVS) – NGC 2392
Likewise, the TVS images of the photospheric helium lines of NGC 2392 are presented
along with their accompanying greyscale images, as well as the TVS/greyscale images
of the He i λ 5875.62 wind line and the deep-photospheric C iv λ 5801.33 line: the pho-
tospheric helium lines of He i λ 4026.19 and He i λ 4471.48 give 95% confidence responses
between −200 and +150 km s−1 and −250 and +150 km s−1 respectively; the He i λ 5875.62
wind line shows a response between −250 and +100 km s−1; and the C iv λ 5801.33 line
gives a response in the ±100 km s−1 range, see Table 5.11.
Table 5.11. NGC 2392 TVS velocity rangesSpectral Line TVS Velocity Range [km s−1]
He i λ 4026 −150 – −50He i λ 4471 −150 – +100He i λ 5876 −200 – +100C iv λ 5801 +50 – +100
5.4. Time Variable Characteristics of the CSPN Winds 195
5.4.7 Fourier Analysis & Signal Selection
The optical time-series spectra is fed into the Fourier2d analysis code (as used with the
UV time-series spectra of NGC 6543 in Chapter 3), where each ion species previously
analysed via TVS is now investigated for possible indications of variability modulation.
The velocity range for the Fourier analysis for each individual ion species is restricted to
the approximate range for which the TVS analysis indicated a response above the 95%
confidence line; this restriction of the velocity range will focus specifically on the extent
of the variance and so should therefore limit the amount of noise undergoing the Fourier
analysis and so the power spectra outcome should be optimally devoid of noise-based
interference which might otherwise produce misleading frequency signals.
Once the Fourier power spectra have been obtained then follows the task of examining
all the Fourier responses from all absorption lines investigated to see whether any potential
modulation signals can be uncovered. In order to do this a selection strategy has to set
in motion, whereupon the frequency signals obtained for each absorption are subjected to
key questions, and depending whether such criteria are met or not, each power spectra
peak is either forwarded for further consideration or abandoned.
The key questions are:
• Has the peak in power (at said frequency) been derived from a Fourier analysis
response from within the wavelength/velocity range of the absorption trough itself, and
not from ‘outside’ where the peak may have originated due to fluctuations in noise-levels?
• Does the power spectra peak appear at (or within ±0.2 (d−1)) any potential window
functions?
• Does the particular peak frequency appear in the Fourier analysis results of more
than one line?
• Does the frequency – and hence the subsequent time period – lend itself to a greyscale
reproduction of a coherently time-modulated signal?
The window functions are those significant time periods of the observation windows
from which the corresponding frequencies can become imprinted upon the Fourier-based
analysis. For instance the data gathered for this optical analysis was gathered over three
nights and so the frequency corresponding to the period of 3 days (i.e f ∼ 0.33 d−1)
might produces an strong response which would be undesirable as it would not reflect
any true modulation periods within the object(s) being studied. Similarly as each period
5.4. Time Variable Characteristics of the CSPN Winds 196
Table 5.12. Hen 2-138: Fourier power spectra peak frequenciesSpectral Line Strongest Frequency Signals [d−1]
He i λ 4026 1.31250 1.72500 3.02500He i λ 4471 1.27500 1.70000 2.90000He i λ 5876 1.32500 2.13750 2.77500
of observation is begun at approximately the same time each evening, the frequency cor-
responding to the times period of 24 hours (i.e. f ∼ 1.00 d−1) might also produce an
misleading response. The duration of an individual objects observation might produce yet
another false frequency, or rather a short range of frequencies which one must be wary of:
on each night NGC 2392 was observed for 3-3.5 hours (6.85 < f < 8.00 d−1); Hen 2-131
and Hen 2-138 were observed (alternating between the two) over a total period of 6-6.5
hours (3.69 < f < 4.00 d−1).
Only when a suspected frequency power peak can satisfy the above criteria can it be
put forward as an indication of a possible modulation period in the absorption profile
variability.
5.4.8 Fourier Analysis – Hen 2-138
Considering the Fourier output power spectra, having been passed through the CLEAN
algorithm (Roberts et al. 1987), the peaks remaining may suggest periodic frequencies if
potential modulation within the outflow of Hen 2-138, particularly of similar frequencies
appear for more than one absorption line under analysis (assuming that the frequency
noted has not been imposed upon the output by any possible window functions). The
central frequency values of any given peak are read of an out ASCII file which lists in two
columns the frequency (in steps of 0.01250 d−1) and its corresponding power value so that
one can track where a particularly strong peak rises to a maximum power before falling
back down again. Although the peak frequency can be thus ascertained to the nearest
0.01250 step, an error margin can be estimated from a given peak’s FWHM i.e. an error
of ± HWHM, which amongst the peaks observed give FWHMs of between 0.3 and 0.4,
suggesting a maximum error margin in frequency of ± 0.2 d−1.
Listed in Table 5.12 are three peak power frequencies observed in the Fourier output
power spectra for the photospheric lines of He i λ 4026.19 and He i λ 4471.48, as well as
the optical wind line of He i λ 5875.62. The output spectra for photospheric helium lines
as well as other metal lines in the optical spectra are shown in Figure 5.25. It was
5.4. Time Variable Characteristics of the CSPN Winds 197
observed that the strongest peaks were obtained for the helium lines, both from the near
photospheric region as well as the base of the wind; other metal lines tended to produce
much shallow peaks whose relative power was at least an order of magnitude less than that
of the stronger helium signals. Therefore it was decided that the search for modulation
frequencies/periods would focus upon the stronger helium lines. The difference in relative
strength between the power spectra outputs for the stronger helium lines and, by way of
example, the output for the metal line of C iv λ 5801.33 is shown in Figure 5.26.
As discussed above in the key questions that need to be addressed when seeking strong
modulation signals, it is necessary to observe a given peak frequency in more than one line
before the signal can be seriously considered. This appears to be the case with the lines
of He i λ 4026.19 and He i λ 4471.48, with both showing strong peaks at approximately 1.3
and 1.7 d−1: these frequencies correspond to periods of 0.77 d and 0.58 d respectively.
A third shallower peak is also visible for both lines at around 3.0 d−1 for the former
line, and at around 2.9 d−1 for the latter: likewise corresponding to periods of 0.33 d
and 0.35 d respectively. These last two peak frequency values are noticeably close to one
another, within less than the ±0.2 d−1 error margin of the Fourier power spectra display:
it is therefore reasonable to ‘average’ their corresponding periods of 0.33 d and 0.35 d –
resulting in a third potential modulation test-period of 0.34 d.
In earlier research (Prinja et al. 2010), it was reported that there are alias peaks at
1.4 and 2.8 d−1, but this result has not exactly been repeated in more recent analysis.
However it should be noted that the lower twin peaks lie either side of an average peak
at approximately 1.4 d−1 and the latter two peaks lie either side of an average of 2.8 d−1.
Perhaps this second analysis has produced power spectra of a greater resolution, that is the
earlier analysis being of a lower resolution has contrived to suggest alias frequents which
on closer inspection may not be as coincidental as at first thought, although the more
recent peaks lie within a reasonably close distance to the former values of these ‘aliases’.
5.4.9 Fourier Analysis – Hen 2-131
As in the Fourier analysis of Hen 2-138, the strongest power spectra responses for Hen 2-131
arose in the analyses of the photospheric helium lines of He i λ 4026.19 and He i λ 4471.48
and the wind line of He i λ 5875.62: as detailed in Table 5.13 the two photospheric lines
provide peak power signals at frequencies at ∼ 2.4 d−1, ∼ 3.5 d−1, and ∼ 4.4 d−1, which
correspond to potential modulation periods of 0.43, 0.30, and 0.23 d respectively. Likewise
5.4. Time Variable Characteristics of the CSPN Winds 198
Table 5.13. Hen 2-131: Fourier power spectra peak frequenciesSpectral Line Strongest Frequency Signals [d−1]
He i λ 4026 2.35000 3.47500 4.38750He i λ 4471 2.35000 3.55000 4.50000He i λ 5876 2.77500 3.62500 4.51250
the He i λ 5875.62 wind line shows its peak frequencies at ∼ 2.8 d−1, ∼ 3.6 d−1, and ∼ 4.5
d−1 which, within the ± 0.2 d−1 error of the FWHM of the power spectra peaks for the
photospheric absorption lines, and hence, correspond to similar periods.
A better comparison of the separate power spectra for the different lines is afforded
when the power spectra are superimposed upon one another to see whether frequency
peaks can be found in roughly the same positions for different resonance lines.
5.4. Time Variable Characteristics of the CSPN Winds 199
2.0
3.0
4.0
5.0
6.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.70.80.80.90.91.01.0
Flu
x
1.0
2.0
3.0
4.0
5.0
6.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.70.80.80.90.91.01.0
Flu
x
Fig. 5.19. TVS analysis plots (below) of the absorption profile of the He i λ 4026(l) and He i λ 4471 (r) optical lines of Hen 2-138, where the upper panel of eachTVS profile depicts the variance statistic, with changes above the 95% significancelevel (dotted line) highlighted. The corresponding greyscale depiction of each lineprofile’s time-series spectra is also shown (above) depicting the temporal changesin the (vertically stacked) individual spectra, all normalised by the correspondingmean profile as shown in the lower panel beneath the TVS significance profile;the dynamical range of the greyscales on this page – and all subsequent greyscalesin this chapter – is 0.95 (black) to 1.05 (white).
5.4. Time Variable Characteristics of the CSPN Winds 200
1.0
2.0
3.0
4.0
5.0
6.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.8
1.0
1.2
1.4
Flu
x
1.0
1.5
2.0
2.5
3.0
3.5
4.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.9
0.9
1.0
1.0
Flu
x
Fig. 5.20. TVS analysis plots (below) of the absorption profile of the He i λ 5876(l) and C iv λ 5801 (r) optical lines of Hen 2-138; the corresponding greyscaledepiction of each lines time-series spectra is also shown (above).
5.4. Time Variable Characteristics of the CSPN Winds 201
2.0
4.0
6.0
8.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.8
0.9
1.0
1.1
1.2
Flu
x
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.8
1.0
1.2
1.4
1.6
1.8
Flu
x
Fig. 5.21. TVS analysis plots (below) of the absorption profile of the He i λ 4026(l) and He i λ 4471 (r) optical lines of Hen 2-131; the corresponding greyscaledepiction of each lines time-series spectra is also shown (above).
5.4. Time Variable Characteristics of the CSPN Winds 202
5.0
10.0
15.0
20.0
25.0
30.0
35.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
1.0
2.0
3.0
4.0
5.0
6.0
Flu
x
1.0
2.0
3.0
4.0
5.0
6.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.9
0.9
1.0
1.0
Flu
x
Fig. 5.22. TVS analysis plots (below) of the absorption profile of the He i λ 5876(l) and C iv λ 5801 (r) optical lines of Hen 2-131; the corresponding greyscaledepiction of each lines time-series spectra is also shown (above).
5.4. Time Variable Characteristics of the CSPN Winds 203
1.0
1.5
2.0
2.5
3.0
3.5
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.9
0.9
1.0
1.0
Flu
x
1.0
1.5
2.0
2.5
3.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.90.90.90.91.01.01.0
Flu
x
Fig. 5.23. TVS analysis plots (below) of the absorption profile of the He i λ 4026(l) and He i λ 4471 (r) optical lines of NGC 2392; the corresponding greyscaledepiction of each lines time-series spectra is also shown (above).
5.4. Time Variable Characteristics of the CSPN Winds 204
1.0
2.0
3.0
4.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
0.9
0.9
1.0
1.0
Flu
x
1.0
1.5
2.0
2.5
3.0
(TV
S)1/
2 (%
FC)
−400 −200 0 200 400Velocity (km/s)
1.0
1.0
1.0
1.0
1.1
Flu
x
Fig. 5.24. TVS analysis plots (below) of the absorption profile of the He i λ 5876(l) and C iv λ 5801 (r) optical lines of NGC 2392; the corresponding greyscaledepiction of each lines time-series spectra is also shown (above).
5.4. Time Variable Characteristics of the CSPN Winds 205
Fig. 5.25. A display of Fourier power spectra for the optical resonance lines ofHen 2-138: the black shows the uncleaned power spectra and the red shows thecleaned power spectra.
5.4. Time Variable Characteristics of the CSPN Winds 206
Fig. 5.26. Fourier power spectra (left) of the C iv λ 5801 deep photospheric line,and the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of Hen 2-138:the uncleaned power spectra is shown in black, with the corresponding cleanedspectra superimposed in red; Cleaned power spectra of the aforementioned opticallines are also shown separately (right). The dotted lines indicate the windowfunction frequencies which may provide false power peaks.
Fig. 5.27. A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,He i λ 4471, He i λ 5876 optical lines of Hen 2-138 over -plotted upon each other –the aim is to strengthen any potential periodicity in the variability by identifyinga peak frequency in more than one line.
5.4. Time Variable Characteristics of the CSPN Winds 207
Fig. 5.28. A display of Fourier power spectra for the optical resonance linesof Hen 2-131: the black shows the dirty power spectra and the red shows thecleaned power spectra.
5.4. Time Variable Characteristics of the CSPN Winds 208
Fig. 5.29. Fourier power spectra (left) of the C iv λ 5801 deep photospheric line,and the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of Hen 2-131:the uncleaned power spectra is shown in black, with the corresponding cleanedspectra superimposed in red; Cleaned power spectra of the aforementioned opticallines are also shown separately (right). The dotted lines indicate the windowfunction frequencies which may provide false power peaks.
Table 5.14. NGC 2392: Fourier power spectra peak frequenciesSpectral Line Strongest Frequency Signals [d−1]
He i λ 4026 2.35000 3.31250 4.28750He i λ 4471 2.35000 3.31250 4.27500He i λ 5876 2.63250 3.31250 4.26250
5.4.10 Fourier Analysis – NGC 2392
PN NGC 2392 is similarly analysed and the results presented below. In initial analysis this
appears to show a very strong correlation in the power spectra for all lines, at a frequency
of approximately 7.5 d−1. In actual fact the obvious correlation is rather too strong and
so a close look at the frequency value for the strongest peaks is required, and it it noted
that the resultant value is actually closely attuned to the times the observations of the
data were undertaken over the three nights of the run. As exposures were taken of this
object during the first 3 – 3.5 hours of the nights session for three nights this repetition
has embedded itself in the data, as this ∼3 hour window function had imposed this ∼ 7.5
d−1 frequency upon the power spectra, thereby overpowering any actual true modulation
frequency/periodicity which might otherwise make a greater impression upon the analysis
tool.
5.4. Time Variable Characteristics of the CSPN Winds 209
Fig. 5.30. A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,He i λ 4471, He i λ 5876 optical lines of Hen 2-131 over -plotted upon each other –the aim is to strengthen any potential periodicity in the variability by identifyinga peak frequency in more than one line.
However, repeated analysis, but with a higher maximum frequency of 20 d−1, has
not produced such a strong response as the above window function, especially when one
plots the power spectra for only the range up to 10 d−1 in order to focus upon lower
frequencies of the photospheric helium lines which, in the other PNs of this chapter,
have demonstrated relatively strong peaks within the 0 – 5 d−1 range in the other Fourier
analyses of their respective optical time-series spectra. There are strong frequency response
from both the He i λ 4026.19 and He i λ 4471.48 photospheric lines at ∼ 2.4 d−1, ∼ 3.3 d−1,
and at ∼ 4.3 d−1. The He i λ 5875.62 low wind line produces a slightly different lowest
frequency response at ∼ 2.6 d−1 but this is within the ± 0.2 d−1 margin indicated by
the FWHM of the frequency responses; the other two strong responses are similar to the
corresponding responses from the photospheric helium lines, of ∼ 3.3 d−1, and at ∼ 4.3
d−1. Consequently, these frequencies give corresponding (potential) modulation periods
of 0.43, 0.30, and 0.23 d.
5.4.11 Greyscale Representations of Phased Periods – Hen 2-138
The time-series spectra of Hen 2-138 of the key helium line profiles are again fed into
the greyscale algorithm, but now the pictorial output can be phased over the key periods
indicated by the peak frequencies as displayed in their respective Fourier power spectra.
Each of the three aforementioned potential modulation periods: 0.77 d, 0.58 d, and 0.34
5.4. Time Variable Characteristics of the CSPN Winds 210
Fig. 5.31. A display of Fourier power spectra for the optical resonance lines ofNGC 2392: the black shows the uncleaned power spectra and the red shows thecleaned power spectra.
d, are thereby ‘greyscale-tested’. The period which demonstrates the greatest coherency
is the latter 0.34 d period, see Figure 5.34: both the He i λ 4026.19 and the He i λ 4471.48
lines appear to exhibit a periodic consistency in their features migrating from bluer to
redder velocities over this repeated period; the higher wind He i λ 5875.62 line, on the
other hand, does not show a similar degree of coherency – it appears relatively fragmented
over this period – and so it cannot be concluded that its structural changes are modulated
over this timescale.
This shorter 0.34 d period would be repeated approximately 6 times over the 2.2 d of
the observation.
5.4. Time Variable Characteristics of the CSPN Winds 211
Fig. 5.32. Fourier power spectra (left) of the C iv λ 5801 deep photospheric line,and the He i λ 4026, He i λ 4471 and He i λ 5876 deep-wind lines of NGC 2392:the uncleaned power spectra is shown in black, with the corresponding cleanedspectra superimposed in red; Cleaned power spectra of the aforementioned opticallines are also shown separately (right). The dotted lines indicate the windowfunction frequencies which may provide false power peaks.
5.4.12 Greyscale Representations of Phased Periods – Hen 2-131
The time-series spectra of the individual line profiles of Hen 2-131 are similarly inputted
into the greyscale algorithm and phased over each of the potential modulation periods
corresponding to the stronger frequencies observed in the Fourier analysis of the helium
lines. The resulting representation which shows the greatest degree of coherency is that
data which has been phased over the period of 0.43 d, see Figure 5.35. As in the similar
phased greyscale image of Hen 2-138 it is possible to observe dark absorption features
migrating towards the red. Also, in the He i λ 5875.62 wind line, one observes features
which appear to migrate in opposite directions: one from blue to red (as seen in the
photospheric lines of Hen 2-138); but also a feature which migrates from redder to bluer
velocities – in a similar fashion to the DAC-like features observed in the UV spectra of
the two previous chapters.
For Hen 2-131, a modulation period of 0.43 d would be repeated approximately 5 times
over the 2.2 d duration of the observation.
5.4. Time Variable Characteristics of the CSPN Winds 212
Fig. 5.33. A display of the cleaned power spectra of the C iv λ 5801, He i λ 4026,He i λ 4471, He i λ 5876 optical lines of NGC 2392 over -plotted upon each other –the aim is to strengthen any potential periodicity in the variability by identifyinga peak frequency in more than one line.
5.4.13 Greyscale Representations of Phased Periods – NGC 2392
When the time-series quotient line profiles for the He i λ 4026.19, He i λ 4471.48 and He i λ 5875.62
lines are once again reproduced via greyscale, but with the representations phased over
each prospective modulation period, the more coherent images of the travelling of feature
within the profiles are those phased on the 0.23 d period, shown in Figure 5.36. However,
in contrast to the similar representations of the line profiles of Hen 2-138, this coherency is
stronger in the 3-cycle greyscale of the He i λ 5875.62 profile; the corresponding greyscale
images of the photospheric helium lines are not as well reproduced.
Similar greyscale representations are also shown of the similar profiles – Figure 5.37 –
but phased over a period of 0.30 d, where again the He i λ 5875.62 profile shows the greater
coherency over this period.
5.4. Time Variable Characteristics of the CSPN Winds 213
The modulation period of 0.23 d would be repeated approximately 9 times over the
2.2 d duration of the observation; the 0.30 d period would be repeated approximately 7
times.
5.4
.T
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Fig. 5.34. Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r) deep-wind lines of Hen 2-138, in whichthe data has been ‘folded’ over a period of 0.34 days.
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Fig. 5.35. Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r) deep-wind lines of Hen 2-131, in whichthe data has been ‘folded’ over a period of 0.43 days.
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Fig. 5.36. Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r) deep-wind lines of NGC 2392, in whichthe data has been ‘folded’ over a period of 0.23 days.
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Fig. 5.37. Greyscale display of the He i λ 4026 (l), He i λ 4471 (c), and He i λ 5876 (r) deep-wind lines of NGC 2392, in whichthe data has been ‘folded’ over a period of 0.30 days.
5.5. Discussion 218
5.5 Discussion
From a desire to obtain more data upon other CSPNs – promoted by the lack of available
time-series data for such objects – I have been given the opportunity to observe and analyse
temporal phenomena with a deeper (nearer-photospheric) region of the stellar wind, where
as well as the wind P Cygni line of He i λ 5875.62, the data has provided the means –
through the (in-house) reduction and subsequent analysis of more photospheric helium
species, particularly the absorption lines of He i λ 4026.19 and He i λ 4471.48, as well as
photospheric metal lines e.g. C iv λ 5801.33.
The various analyses presented in this chapter indicate that the PN He 2-138 pos-
sesses a dense, slow moving outflow indicated by the blueshifted Si iii triplet found in the
densest super-photospheric regions of a stellar atmosphere. Whereas similar blueshifted
Si iii triplet profiles are observable in the UV spectra of Hen 2-131 and suggest a similar
conclusion; the UV spectra of NGC 2392 show much shallower/weaker absorption profiles,
with the Si iii triplet exhibiting little in the way of P Cygni-type wind signature, although
possible marginally blueshifted.
The SEI resonance line model fits suggest that Hen 2-138 possesses a dual-component
wind: the lower ion species of Al iii λ 1854.72 and S iv λ 1072.97 are modelled with a
wind terminal velocity of 300 km s−1, whereas the higher ion species of C iv λ 1548.20 and
Si iv λ 1393.76 required the requisite wind terminal velocity parameter for SEI stepped up
to 700 km s−1 in order for a decent model fit.
Similar SEI modelling undertaken on UV data (from IUE and FUSE) of the central
stars of Hen 2-131 and NGC 2392 have been carried out with, for the most part, a ter-
minal wind velocity of 400 km s−1; the only exceptions were a slight increase to v∞= 450
km s−1 for the S iv λ 1072.97 (red) component, and a larger increase to 600 km s−1 for the
Si iv λ 1393.76 (blue) component. These being the only exceptions, there was not enough
evidence to suggest the existence of a dual-velocity nature to the wind of either central
star, and indeed such a conclusion has not been seen in any of the literature pertaining to
these two objects.
Further line synthesis modelling of Hen 2-138, via CMFGEN, has indicated that the
outflow has a dual-component nature: the CMFGEN analysis for a temperature of a
hotter component (> 29,000 K) provides a better fit to the near-photospheric C iv and
O iii lines, but at the same time predicting too much He ii and not enough He i ; in
5.5. Discussion 219
contrast, a cooler component (∼ 25,000 K) is required to better fit the low ionisation lines
(including C ii and Al iii ), but these models subsequently predict too much photospheric
He i and therefore not enough/is too weak in He ii . The CMFGEN model is unable
to reproduce the relative strengths between the absorption and emission components of
P Cygni profiles, particularly those of the Si iv λλ 1393.76, 1402.77, the C iv λλ 1548.20,
1550.77, and the Mg ii λλ 2795.53, 2802.70 doublets. If this suggests the presence of dual-
nature to the outflow, this would seem to be confirmed in the SEI modelling of some of
the P Cygni resonance lines: for the UV Al iii λ 1854.72 and the S iv λ 1072.97 which as a
lower abundance surrogate to the S iv line in the range if ionisation potential, these lines
can only be modelled with a terminal velocity of 300 km s−1, whereas a more than double
terminal velocity is required for the modelling of the blue component of the S iv λλ 1062.66,
1072.97 doublet, as with the similar component of the C iv λλ 1548.20, 1550.77 doublet.
It is important to note that although the P Cygni profiles modelled have been taken from
a variety of different sources (IUE, FUSE), and hence different epochs, there has been
no recorded shift in the blue edge/wings of the resonance lines which is more than 100
km s−1.
Hybrid winds can often be seen emanating from Be stars, where dual layer outflows
have been modelled: a hotter and higher velocity wind emanates from the polar regions
of the star, its presence revealed through the appearance of strong UV high-excitation
(resonance) absorption profiles; a cooler, lower velocity wind (< 100 km s−1) emerges
from the more equatorial regions, and described by narrow low-excitation emission lines
(Zickgraf et al. 1985). Subsequently the increase from the slower velocity of 300 km s−1
for the Al iii and S iv lines to the much higher (more than double) velocity of the C iv
and Si iv lines suggest a spatial distribution of similarly latitude-dependent outflow which
here is being viewed pole-on. However the apparent absence of the Nv λλ 1238.82, 1242.80
doublet in IUE data lets down this analogy as in a Be star’s wind this doublet would appear
strongly in emission.
Asymmetric wind properties, such as have been considered in this chapter, add to the
ongoing debate concerning the often non-spherical appearance of an increasing number
of young planetary nebulae, many of which exhibit axi- and point-symmetries (Sahai
& Trauger 1998). If the occurrence of the high mass-loss superwind towards the end
of the AGB stage is asymmetric then the subsequent interaction between the wind and
the circumstellar material will likewise be asymmetric, which may result in a complex
5.5. Discussion 220
nebula. The HST images of Hen 2-138 and Hen 2-131 both show non-spherically symmetric
formations: the former has an overall elliptical shape with many bubble-like structures
along its outer edge, appearing in a point-symmetry arrangement around the central star;
the latter is less elliptic, also with bubble-like structures along its edge, but not in as
complex an arrangement as in Hen 2-138.
One theoretical mechanism leading to an asymmetric outflow is the creation of a sub-
surface magnetic dynamo, born out of a significant differential rotation between the con-
tracting core and expanding envelope of an AGB star, with a transfer of angular momen-
tum speeding up the core’s rotation while slowing down that of the envelope (Blackman
et al. 2001). The effect of rapid rotation upon line-driven outflows can lead to a latitude
dependent mass-loss rate, which is itself dependent upon the surface radiative flux and
effective surface gravity which, when gravity darkening is taken into account, is much
greater at the poles than at the equator (Dwarkadas & Owocki 2003; Dwarkadas 2004),
causing an asymmetric outflow and evolving into a bipolar nebula. Indeed, the apparent
asymmetry of the Hen 2-138 outflow might be attributed to the central star being a rapid
rotator, with the added dichotomy of the CMFGEN fitting possibly indicating that one is
observing the central star from a point somewhere between the hotter, faster polar wind,
and the cooler, slower equatorial outflow.
It has been suggested that the formation and evolution of non-spherical nebulae may
sometimes be caused by binary systems, and that around 15% of planetary nebulae are
part of a short period (< 3 days) binary system (Bond 2000); however other radial
velocity-based survey of CSPNs have provided binary system estimates of around 40-60%
(Sorensen & Pollacco 2003), or even over 90% (De Marco et al. 2004). The deep-seated
near-photosperic lines studied in this chapter have shown that although they exhibit clear
variability in that their enhanced absorption features migrate from the blue towards the
red, seen particularly in the temporal variability exhibited by Hen 2-138 and the patterns
displayed for the He i λ 4026.19, He i λ 4471.48 lines, these do not possess the more sinu-
soidal side-to-side pattern of a more regular radial velocity shifts. Instead these may depict
prograde non-radial pulsations (NRPs), and indeed, as the migration shown is blue-to-red,
such features cannot be attributed to the effects of a stellar wind which would cause ab-
sorption feature migration from red-to-blue velocities; the prescence of the wind can only
be seen in the more clearly defined P Cygni profiles as seen in the He i λ 5875.62 line and
the UV resonance lines of the IUE (UV) and FUSE (FUV) spectra.
5.5. Discussion 221
The temporal analysis of three nights’ time-series data, obtained from the ESO 3.6m
optical telescope and the HARPS spectrograph, have enabled the investigation into temporally-
variable phenomena located towards the near-photospheric base of the wind. Indeed,
structure has been observed in this region for all three objects, and for each Fourier pe-
riodogram analysis has been applied to the time-series data of the helium lines as well as
other metal lines (e.g. the deep-wind C iv λ 5801.33 absorption line). The strongest power
responses of potential modulation frequencies were attributable to the photospheric helium
lines, and through a stepped selection process, subsequent modulation periods have been
tested via their application to a period-phased greyscale imaging process. This has had
the result that the aforementioned helium lines of Hen 2-138 have been greyscale-phased
over a period of ∼0.34 days; Hen 2-131 over a period of ∼0.48 days; and NGC 2392 over
a period of ∼0.23 days, with a second potential modulation period of ∼0.30 days.
It has been observed that these time-series studies of young, H-rich CSPNs have pro-
vided evidence of potentially modulated structures within the lower wind regions, and,
as seen in the blue to red migrations of lines He i λ 4026 and He i λ 4471, if such fea-
tures are evidence of non-radial pulsations (NRPs), these might provide the origins of
photospherically-originating structures, carried outwards from the central star via co-
rotating interaction regions (CIRs). Fullerton et al. (1996) observed a prolific manifesta-
tion (77% of their sample) of variability in photosperic absorption line profiles in optical
spectra of O stars, variability which quite possibly arises from NRPs; and in considering
the similarly wide proliferation of O stars exhibiting variable winds, demonstrated by the
appearances and migrations of DACs in UV P Cygni profiles, the possibility of a physical
connection between the two is proposed. Cranmer & Owocki (1996) have also considered
a connection between photospheric disturbances and the appearances and migrations of
DACs further out in the stellar wind: their proposed mechanism is the aforementioned
CIRs – the interface between co-rotating ‘streams’ of higher and lower density material,
spreading out spirally from the stellar surface, caused by so-called bright spots (low veloc-
ity - high density), and dark spots (high velocity - low density); the fast streams collide
with the slower streams, the resulting shock interaction producing a plateau in the velocity
gradient, and a subsequent localised increase in the absorptive optical depth.
de Jong et al. (2001) speculate upon the action of CIRs providing a connection between
their role in the manifestation and recurrence of DACs in UV resonance line profiles and
similarly varying, i.e. coincidental in phase, with maxima in blue-shifted Hα profiles – a
5.5. Discussion 222
connection which leads to the suggestion that the variability observed in the stellar wind
must originate near the stellar surface, and that the action of the CIR model is a viable
mechanism by which to transport the density-related markers of such surface disturbances.
They consider small magnetic field structures as a possible cause of the perturbation effects
upon the surface, however their magnetic field measurements prove inconclusive; likewise
in considering the possibility of NRPs providing the causal mechanism for the surface
density disturbances – to be carried into the UV wind regions via CIR spirals – these
results are also inconclusive in that the recorded NRP period of around 3.5 hours is much
faster than the modulation period observed in the appearance of DACs, at around 2.1
days.
Chapter 6
Conclusion
6.1 Structure in Stellar Winds
The prime motivation for this thesis was to explore whether the stellar outflows of H-rich
central stars of planetary nebulae possessed a degree of structure such as that has been
observed within the outflows of the hotter and more massive O stars.
Firstly, time-series UV spectra obtained for the Cat’s Eye Nebula, NGC 6543, from
the archive of the Far Ultraviolet Spectroscopic Explorer was examined for evidence of
stellar wind variability and it was found that the outflow emanating from the central star
is exhibits unsaturated P v P Cygni profile variability on a time-scale of hours in the
form of recurrent additional optical depth absorption features which are seen to migrate
blueward through the absorption troughs. This DAC-like behaviour is similar to that
exhibited by the presence of DACs in UV data of hot, luminous OB stars. In comparing
the ‘DAC-like’ properties of NGC 6543, as seen in this study, to those formerly observed
in various studies of OB stars (e.g. Kaper et al. 1996; Prinja 1998; Fullerton et al. 2006b),
the parameters are remarkably similar, including the flow-time-scaled (linear) acceleration
of ∼ 26 km s−1 for NGC 6543, when the similar acceleration of an example O star is of the
same order at ∼ 10 km s−1.
In order to investigate whether this similarity in the physicality of the respective out-
flows is just coincidental for NGC 6543 alone, or not, the following chapter was concerned
with trying to observe similar variable phenomena – the blueward-migrating DAC-like fea-
223
6.1. Structure in Stellar Winds 224
tures appearing within the absorption troughs of the Pv λλ 1118, 1128 doublet – could be
observed in the outflows of other CSPNs. However time-series UV spectra is limited and
so of four other CSPNs has been subjected to similar time-variance analysis techniques:
the TVS analysis had been applied to the time-series spectra available and subsequent
greyscale displays have provided image-based representations of the variability contained
therein. Of the four central stars examined, blueward migrating DACs were observed in
the temporal greyscale images of the (limited) UV spectra for two objects, namely NGC
6826 and IC 2149, the DAC-like structures of both of which were measured as to their
blueward velocity migration in time, and for which the former was shown to possess a
flow-time-scaled approximate (linear) acceleration of ∼25 km s−1, and ∼29 km s−1 for the
latter – both close to the ∼ 26 km s−1 measured for NGC 6543. The similarities of flow-
time acceleration suggest that might be a typical value i.e. ∼ 20 km s−1 for CSPNs in
general, but without more extensive time-series – certainly not the wealth of UV spectra
as available for O stars – this would be difficult to prove. Nevertheless, it does goes further
to suggest the possibility of a common frame of reference for CSPN DAC-like behaviour.
The lack of extensive UV time-series data available for CSPNs has prompted the in-
vestigation into the optical wavelength range and therefore able to observe and analyse
temporal phenomena in the nearer-photospheric region of the stellar wind. Here the
sole P Cygni wind line is that of He i λ 5875.62, however analysis of other photospheric
helium lines within this region, particularly the absorption lines of He i λ 4026.19 and
He i λ 4471.48, as well as photospheric metal lines e.g. C iv λ 5801.33 allow the investiga-
tion of potential variability at the base of the wind.
The SEI resonance line model fits (of single UV exposures only) suggest that Hen
2-138 possesses a dual-component wind: the lower ion species of Al iii λ 1854.72 and
S iv λ 1072.97 are modelled with a wind terminal velocity of −300 km s−1, whereas the
higher ion species of C iv λ 1548.20 and Si iv λ 1393.76 required the requisite wind termi-
nal velocity parameter for SEI stepped up to −700 km s−1. Subsequent analysis by Miguel
Urbaneja (IfA, Hawai’i), using CMFGEN, confirms a higher/lower velocities are required
to match higher/lower ion species, hinting at a laterally-dependent outflow or ‘hybrid’
wind. SEI modelling for the central stars of Hen 2-131 and NGC 2392 have not provided
evidence to suggest a dual-component wind of either central star, both allowing (for the
most part) modelling of wind profiles with a terminal velocity of v∞ = −400 km s−1.
However, the temporal analysis of three night’s time-series data, obtained from the
6.1. Structure in Stellar Winds 225
ESO 3.6 m optical telescope and the HARPS spectrograph, has enabled the investigation
into temporally-variable phenomena located towards the near-photospheric base of the
wind. Indeed, structure has been observed in this region for all three objects and for each
Fourier periodogram analysis has been applied to the time-series data of the helium lines as
well as other metal lines (e.g. the deep-wind C iv λ 5801.33 absorption line). The strongest
power responses of potential modulation frequencies was attributable to the photospheric
helium lines and subsequent modulation periods have been tested via their application to
a period-phased greyscale imaging process with the result that the aforementioned helium
lines of Hen 2-138 have been greyscale-phased over a period of ∼0.35 days; Hen 2-131 over
a period of ∼0.48 days; and NGC 2392 over a period of ∼0.23 days, and also a second
potential modulation period of ∼0.30 days.
The modulation of the seemingly blue-to-red structures, as observed in the phased
greyscales of Hen 2-138, are interesting in that they might suggest the manifestation of
Non-Radial Pulsations (NRPs), which may or may not provide the photospheric mech-
anism responsible for the density fluctuations which travel through the stellar outflow
via Co-Rotating Interaction Regions (CIRs). As movement of these regions in the outer
wind are observed by the motions of Discrete Absorption Components (DACs) which are
observed to migrate through the absorption troughs of UV spectra. The modulated move-
ments of these structure have been observed ubiquitously in the UV spectra of winds
from OB stars. The outflows of CSPNs have also demonstrated variable winds in that
UV spectroscopic exposures, taken months or years apart, have also shown changing ab-
sorption profiles of UV resonance lines. However, without extensive time-series UV data,
investigations into wind-born structures have not been carried out to the extent that they
have been for OB stars (although similarities between the winds of H-rich CSPNs and OB
stars has been suspected since the initial discoveries of the changing shape of the CSPN
P Cygni resonance line profiles). With the availability of FUSE time-series UV data, the
more temporally-based spectroscopic study of the variable stellar wind of CSPNs has be-
gun, and the early indications are that, in terms of the modulated behaviour of their UV
outflow, central stars are more closely akin to OB stars than previously thought.
6.2. Future Work 226
6.2 Future Work
It has also become apparent in recent years that a quantitative of the clumped nature of
a stellar wind would confirm the suspicion that it is the existence of structure within a
porous wind – and therefore not smooth as previously assumed – that is a key ingredient
in the manifestation of such phenomena as XUV ionisation and X-rays (Oskinova et al.
2007).
Sobolev with Exact Integration (SEI) resonance line profile modelling, which has been
used extensively in the work behind this thesis assumes a smooth, homogenous wind, and
takes no account of clumping – whereas it has been shown that clumping, and by extension
porosity, must be taken into account in order to be able to accurately model line profiles
in the wind (e.g. Bouret et al. 2005; Kudritzki et al. 2006; Oskinova et al. 2007).
To this end the Si iv λλ 1393.76, 1402.77 doublet, taken from UV data of B supergiants,
has been analysed in terms of the ratios between the two components (Prinja & Massa
2010). A better understanding of the relationship between the doublet components is key
to understanding the nature of the density of the stellar wind: for a smooth, homogeneous
wind, the ratio of the optical depths as modelled from the absorption troughs of the doublet
components should be equal to the ratio between their respective oscillator strengths. If,
however, the star was partially obscured by optically thick clumps, then the ratio between
the components would be ∼ 1, as the radial optical depth would only depend upon the
covering factor of the clumps, which would therefore reduce the doublet ratio by a factor
of between 1 and 2.
A key criterion in seeking suitable data, as well as possessing well-developed but un-
saturated absorption troughs, is the velocity separation of the two components of the Si iv
doublet, namely whether they possess (wind) terminal velocities which are less than 0.5
of the velocity separation between the two: if so, then two two components of the doublet
can be modelled separately, that is, as if they were two singlets, and hence radiatively
decoupled.
The absorption profile modelling is undertaken using the SEI method, and as the
two components are able to be modelled as singlets, the modelling process provides a
set of τrad(w) for each component, which can then be combined to produce a this set
of τbluerad (w)/τ red
rad (w). Only τrad(w) values of between 0.3 – 5.0 were considered so as to
avoid lines either too weak or saturated. It is reported that in the vast majority of cases
6.2. Future Work 227
the ratios yield values which are less than 2.01 (which would be that expected from a
smooth wind), and the majority range between 1.0 and 1.5, with the average being 1.46,
so it would seem that the results indicate that a porous, heavily clumped (optically-thick)
wind. It is also noted that the stars are scattered over the temperature ranges from B0 to
B5, and the reduced τrad(w) ratio is seen across (almost) this range, which would indicate
that the reduced ratio phenomena is not dependent upon the temperature of the star.
An alternative method of investigation was employed for those stars whose Si iv dou-
blet separation was in excess of 1000 km s−1, that is they two components could not be
effectively decoupled, and therefore could not be modelled (via SEI) separately. Instead
SEI models were applied for the doublet in the normal manner, but the difference in this
method was that the ratio of the doublet oscillator strengths, f , is now treated as a free
parameter, and adjusted so as to obtain a best-fit for the doublet. Most of these best-fit
f -values are found to be between ∼ 1 and 2. For a fixed mass-loss rate, velocity law and
ion fraction, the f -value (the ratio of the oscillator strengths) for the is the equivalent of
the optical depth ratios for the decoupled doublets. As with the optical depth ratios of
the first group of stars, the results from the second sample, the oscillator strength ratios
between the blue and red components fall between 1.0 and 2.0, with the majority between
1.0 and 1.5, and are therefore comparable with the results of the former set.
As this approach has proven beneficial to the study of B stars, particularly in its
conclusive demonstration of the validity of the concept of the clumped nature of stellar
winds – an assumption which should improve accuracy in the calculation of stellar mass-
loss rates – it would seem pertinent to extend this doublet-ratio approach to the modelling
of P Cygni absorption profiles in the outflows of central stars.
However, in order to be able to carry on this recent development into the nature of
the stellar winds of central stars, and indeed all other aspects of the research outlined
in this thesis, there has to be an extensive wealth of data available – particularly given
the high-quantity exposure-dependence of time-series analysis. Therefore only until the
amount of spectroscopic data available of CSPNs matches the extent of the same for OB
stars will one be able to pursue stellar wind investigations into the former as they have
been for the latter.
.1 Appendix A: SEI Plots of Two DAC Sequences
Presented here are the two sets of eight SEI models corresponding to the two DAC-
progression sequences as mentioned in Chapter 3, and for each the central velocity of the
blueward-migrating DAC was estimated, and subsequent estimates of DAC acceleration
were obtained.
Fig. .1. The first four SEI models of the 1st P v DAC-progressive sequence forHen 2-138: above No. 1 (l), No. 2 (r); below No. 3 (l), No. 4 (r).
.1. Appendix A: SEI Plots of Two DAC Sequences 229
Fig. .2. The second four SEI models of the 1st P v DAC-progressive sequencefor Hen 2-138: above No. 5 (l), No. 6 (r); below No. 7 (l), No. 8 (r).
.1. Appendix A: SEI Plots of Two DAC Sequences 230
Fig. .3. The first four SEI models of the 2nd P v DAC-progressive sequence forHen 2-138: above No. 1 (l), No. 2 (r); below No. 3 (l), No. 4 (r).
.1. Appendix A: SEI Plots of Two DAC Sequences 231
Fig. .4. The second four SEI models of the 2nd P v DAC-progressive sequencefor Hen 2-138: above No. 5 (l), No. 6 (r); below No. 7 (l), No. 8 (r).
.1. Appendix A: SEI Plots of Two DAC Sequences 232
The last (single) SEI model presented is that of the ‘non-DAC case’ from which the
ratio of τDAC/τmin for each corresponding central velocity was derived for each individual
exposure in these two sequences – also detailed in Chapter 3.
Fig. .5. The SEI model of the ‘non-DAC case’.
.2. Appendix B: Full 2-D Fourier Spectra Displays 233
.2 Appendix B: Full 2-D Fourier Spectra Displays
Presented here are the full two-dimensional Fourier analysis plots for Hen 2-138, Hen 2-131,
and NGC 2392 from Chapter 5. Only those lines which produced a substantial response
above the 95 % confidence line in the TVS analysis were then subjected to further Fourier
analysis; therefore not all lines detailed in the previous appendix, are represented here.
.2. Appendix B: Full 2-D Fourier Spectra Displays 234
−150 −100 −50 0 50 100Velocity (km/s)
0.70
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Fig. .6. Full displays of Fourier spectral analysis for Hen 2-138: above He i λ 4026(l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r).
.2. Appendix B: Full 2-D Fourier Spectra Displays 235
−150 −100 −50 0 50Velocity (km/s)
0.8
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1.0
1.1
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0.51.01.52.02.53.0Power x 10−5
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−150 −100 −50 0 50 100Velocity (km/s)
0.8
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1.8
Flu
x
0.20.40.60.81.0Power x 10−4
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200.0
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1.6
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0.51.01.52.02.53.0Power x 10−5
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2.6
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7.4
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Fig. .7. Full displays of Fourier spectral analysis for Hen 2-131: above He i λ 4026(l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r).
.2. Appendix B: Full 2-D Fourier Spectra Displays 236
−150 −100 −50 0 50 100Velocity (km/s)
0.86
0.88
0.90
0.92
0.94
0.96
Flu
x
1 2 3 4 5Power x 10−6
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1.3
2.5
3.7P
ower
x 1
0−6
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−200 −150 −100 −50 0 50Velocity (km/s)
0.85
0.90
0.95
1.00
Flu
x
0.20.40.60.81.01.21.4Power x 10−5
0
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200.1
2.0
3.9
5.9
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er x
10−
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−200 −100 0 100Velocity (km/s)
0.88
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0.98
1.00
Flu
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1 2 3 4Power x 10−6
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1.0
1.9
2.9
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−100 0 100Velocity (km/s)
0.98
1.00
1.02
1.04
1.06
Flu
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1 2 3 4Power x 10−6
0
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10
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200.1
0.8
1.6
2.4
Pow
er x
10−
6
0
5
10
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20
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cycl
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0
5
10
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Fre
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Fig. .8. Full displays of Fourier spectral analysis for NGC 2392: aboveHe i λ 4026 (l), He i λ 4471 (r); below He i λ 5876 (l), C iv λ 5801 (r).
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